REESE  LIBRARY 

01     THK 

UNIVERSITY  OF  CALIFORNIA 


L 


Deceive  J 


Accessions  MT. 


C7.7S.s-  M). 


THE 


VENTILATION  OF   MINES, 


DESIGNED  FOR  USE  IN  SCHOOLS  AND  COLLEGES ; 

AND    FOR    PRACTICAL    MINING    MEN   IN 

THEIR  STUDY  OF  THE  SUBJECT. 


BY 


J.  T.  BEARD,  C.E.,  E.M., 

Iowa  Mining  Exchange,  Ottumwa,  la.  ; 

Secretary  of  the  State  Board  of  Examiners  for 

Mine  Inspectors^  Iowa. 


FIRST    EDITION. 
FIRST    THOUSAND. 


NEW  YORK: 
JOHN     WILEY    &     SONS, 

53  EAST  TENTH  STREET. 
1894. 


Copyright,  1894, 

BY 

J.  T.  BEARD. 


ROBERT  DRUMMOND,    KLECTROTYPER  AND   PRINTER,    NEW  YORK. 


JDefcfcateD 

TO  THE  MINERS  OF  IOWA, 

AMONG  WHOM  THE  AUTHOR  HAS  SPENT  THE  PAST 

THIRTEEN  YEARS  OF  HIS  LIFE. 


PREFACE. 


THE  Ventilation  of  Mines  is  a  subject  to  which  all 
interested,  miners  and  operators  alike,  should  give  the 
most  earnest  heed — miners,  because  upon  the  observ- 
ance of  its  laws  and  principles  depend  their  life  and 
health  ;  operators,  because  a  thorough  knowledge  of 
the  subject,  followed  by  a  faithful  application  of  such 
knowledge  in  practice,  cannot  but  result  in  a  large  sav- 
ing of  expense,  ranging  from  fifty  to  seventy-five  per 
cent. 

It  is  a  subject  to  which  as  yet  American  writers 
have  contributed  little.  This  is  to  be  accounted  for 
partly  on  account  of  the  infancy,  as  it  were,  of  the 
Mining  Industry  in  America,  as  compared  with  its  de- 
velopment in  the  mother  country;  but  largely  on 
account  of  the  inordinate  haste  of  Americans  to  see 
results.  This  haste  is  only  too  apparent  in  all  of  our 
industries,  but  in  none  is  it  more  observable  than  in  the 
mining;  and  one  of  its  most  deplorable  results  is  to 
hinder  and  in  many  cases  render  wholly  impracticable 
scientific  observation.  The  American  operator  with 
but  few  exceptions  adopts  such  appliances  as  first  come 
to  hand,  or  as  suggest  to  him  a  saving  in  first  cost ; 
often  not  caring  for,  or  taking  the  time  necessary  to,  a 
thorough  investigation  as  to  the  comparative  operating 


VI  PREFACE. 

expenses  of  different  appliances.  Very  often  the  ma- 
chinery, fans,  and  other  appliances  brought  into  use 
have  been  purchased  from  some  old  mining  plant  and 
remodelled  and  repaired  with  true  Yankee  skill  and 
ingenuity;  but  the  type  of  construction  is  old  and 
affords  no  opportunity  for  reliable  investigation. 

Such  haste  of  Americans  to  see  results  and  to  make 
a  fair  showing  of  returns  upon  investment  is  therefore 
no  help  to  the  advancement  of  science  ;  and  were  it 
not  for  their  habits  of  close  observation,  their  keen 
perception,  their  practical  skill  and  ingenuity,  they 
could  not  compete  in  the  field  of  scientific  research. 
The  methods  of  Americans  are,  however,  always  prac- 
tical, and  herein  is  their  value. 

The  field  for  scientific  research  among  English  mines 
has  been  larger.  The  mines  as  a  rule  are  deeper  and 
the  mining  plants  present  a  more  permanent  aspect. 
English  writers  have  contributed  more  to  practical 
mining  literature  than  any  others.  Foremost  among 
those  who  have  discussed  the  ventilation  of  mines  are 
Mr.  J.  J.  Atkinson  and  Mr.  W.  Fairley.  There  are 
probably  many  others  worthy  of  note  who  have  con- 
tributed to  increase  our  fund  of  knowledge  in  this 
direction,  but  whose  writings  have  not  become  so  well 
known. 

The  French  have  furnished  some  good  physicists, 
and  their  experiments  and  investigations  of  the  laws 
controlling  the  motion  of  fluids,  etc.,  have  proved  in- 
valuable. The  deductions  of  M.  Murgue,  relative  to 
the  "  Equivalent  Orifice,"  will  be  appreciated  by  math- 
ematicians ;  but,  as  M.  Murgue  says  himself,  it  is  a 
mere  fiction ;  and,  we  may  add,  does  not  rightly  find 
its  application  in  the  ventilation  of  mines. 


PREFACE.  Vll 

What  is  needed  to-day  is  practical  reasoning,  sup- 
ported by  the  results  of  true  scientific  observation. 
The  investigator  must  possess  a  thorough  knowledge 
and  comprehension  of  the  laws  of  physics  :  he  must  be 
a  keen  observer  and  a  logical  reasoner;  above  all,  he 
must  build  his  theories  upon  fact,  never  distorting  the 
fact  to  suit  a  theory.  Every  law  of  physics  acts  con- 
tinuously and  as  though  no  other  law  .existed :  the 
resultant  condition  is  the  algebraic  sum  of  all  the  ex- 
isting conditions.  If  any  of  these  existing  conditions 
are  neglected,  a  true  result  is  not  obtained. 

We  see  reports,  from  time  to  time,  made  upon  so- 
called  scientific  investigations  of  results  under  varying 
conditions ;  giving,  for  example,  the  quantities  of  air 
yielded  by  a  straight  paddle-fan,  discharging  into  a 
certain  mine,  making  a  certain  number  of  revolutions 
per  minute,  and  giving  the  diameter  of  the  fan  ;  but 
stating  no  breadth  of  blade,  no  temperature,  or  barom- 
eter, or  hygrometric  state  of  the  atmosphere  at  the 
time  of  observation.  Although  the  simple  omission  of 
the  last-named  item  would  be  pardonable,  as  its  effect 
is  small,  still,  in  careful  observation,  for  scientific  pur- 
poses, every  affecting  cause  should  be  taken  into  ac- 
count. The  formulas  of  M.  Murgue,  relative  to  the 
fan,  make  no  account  of  the  width  of  the  fan-blade ; 
ignore,  completely  the  questions  of  temperature,  ba- 
rometer, and  hygrometric  state ;  while  it  is  a  well- 
known  fact  that  a  fan  is  less  powerful  in  light  air  than 
when  working  in  a  denser  medium. 

While  it  is  the  author's  aim,  in  the  following  work, 
to  base  all  his  deductions  upon  mathematical  principles, 
working  out  the  same  for  the  benefit  and  satisfaction 
of  the  student,  it  is,  at  the  same  time,  his  desire  to 


Vlll  PREFACE. 

give  to  the  practical  miner  a  book  of  reference,  the 
careful  study  of  which  will  enable  him  to  better  under- 
stand the  conditions  with  which  he  is  surrounded  and 
upon  which  his  health  and  happiness  so  largely  depend. 
As  there  is  at  present  no  American  and  probably  no 
English  work  that  is  well  adapted  for  use  in  schools 
and  colleges,  it  is  hoped  that  this  little  work  may,  to 
some  extent,  prepare  the  way  for  more  extended  and 
complete  text-books  upon  a  subject  of  such  vast  im- 
portance to  the  mining  engineer. 

By  way  of  encouragement,  the  author  would  say  to 
the  student,  where  the  reasonings  or  deductions  lead- 
ing up  to  certain  conclusions  may  at  times  seem  to  be 
difficult,  the  study  of  the  subject  loses  much  of  its 
formidable  aspect  if  taken  up  one  step  at  a  time.  It 
has  been  the  aim  throughout  to  present  the  subject 
step  by  step,  and  to  so  systematize  the  whole  as  to 
maintain  a  constant  and  healthful  growth,  and  by  this 
means  to  prepare  the  mind  for  a  full  and  final  concep- 
tion of  the  whole.  The  processes  of  the  calculus  have 
been  purposely  excluded ;  some  of  the  deductions  en- 
gaging the  study  of  the  author  for  months  at  a  time,  as 
he  has  sought  to  disentangle  them  from  the  intricacies 
of  the  higher  mathematics,  with  which  they  are  almost 
inextricably  associated. 

To  points  wherein  the  author  differs  from  other 
writers  he  has  given  the  most  careful  and  patient 
study ;  and  submits  his  honest  conclusions,  by  no 
means  in  a  spirit  of  controversy,  but  with  a  desire  to 
establish  the  truth  and  determine  the  laws  that  under- 
lie and  form  the  foundation  of  all  mine-ventilation. 

The  author  wishes  to  here  acknowledge  the  courtesy 
and  assistance  of  many  friends,  among  whom  may  be 


PREFACE.  ix 

especially  mentioned  the  State  Mine  Inspectors  of 
Iowa,  who  have  assisted,  by  every  means  in  their 
power,  to  aid  investigation,  and  whose  mature  judg- 
ment has  more  than  once  afforded  valuable  help. 

J.  T.  B. 

OTTUMWA,  IOWA,  December  16,  1893. 


INTRDUCTION 


WHAT  the  author  has  endeavored  to  accomplish  in 
the  following  pages  is  to  make  plain  and  simple  to 
the  practical  mind  the  workings  of  the  laws  which  ani- 
mate and  control  the  ventilating  currents  in  mines. 
These  laws  are  at  times  necessarily  somewhat  complex, 
because  they  express  the  relation  between  force  and  an 
expansive,  fluid  medium.  The  mechanics  which  for- 
mulates the  expressions  of  force,  as  developed  or  trans- 
mitted by  the  rigid  parts  of  machines,  is  simple,  compared 
with  the  cubical  and  quadratic  expressions  involved  in 
the  discussions  of  force  as  applied  to  fluids.  But, 
throughout,  the  endeavor  has  been  made  to  express  in 
simple,  practical  terms  the  results  of  mathematical  cal- 
culation. While  it  is  not  expected  that  the  general 
reader  will  care  to  investigate  the  methods  of  deduction, 
which  require  often  a  knowledge  of  algebra  and  the 
higher  mathematics,  yet  these  methods  have,  for  the 
most  part,  been  given  in  full,  to  demonstrate,  for  the 
benefit  of  the  student,  the  exactness  of  the  conclusions 
reached.  This  has  seemed  particularly  essential,  as 
some  of  the  results  obtained  are  different  from  those 
obtained  by  other  writers. 

It  is  believed  some  flagrant  errors  have  crept  into  our 
mining  formulae,  and  some  of  the  generally-accepted 
facts  are  based  upon  wrong  hypotheses.  For  example, 
in  relation  to  the  action  of  fans,  the  idea  seems  to  be 


xii  INTRODUCTION. 

quite  prevalent  that  the  air-current  partakes  of  the  pe- 
ripheral velocity  of  the  fan-blade  tips,  and  this  becomes 
the  initial  velocity  of  the  current.  Although  this  is 
not  the  expressed  idea  of  Murgue,  yet  even  he  trans- 
mutes the  mechanical  velocity  of  the  fan-blade  into  an 
expression  of  head-of-air-column,  which  leads  him  se- 
ductively to  the  same  error  ;  as  he  continues,  in  the 
course  of  his  reasoning,  to  treat  the  established  veloc- 
ity of  the  current  as  dependent  alone  upon  the  genera- 
tive head-of-air-column  ;  forgetting  that  the  same  head- 
of-air-column  will  produce  a  different  velocity  according 
to  the  conditions  under  which  the  current  is  moving.  In 
other  words,  M.  Murgue  tries  to  assimilate  the  condi- 
tions of  a  current  moving  under  a  resisting  pressure  to 
the  purely  theoretical  case  of  movement  opposed  by 
no  such  resistance.  The  velocity  generated  by  a  body 
falling  through  a  certain  height  varies  as  the  square 
root  of  that  height  ;  the  velocity  of  the  air  in  the  mine 
varies  as  the  square  root  of  the  pressure,  other  factors 
remaining  the  same  ;  hence  it  is  true  that  the  height  gen- 
erative of  any  given  velocity  represents  accurately  the 
pressure  animating  such  velocity  where  no  resistance 
is  opposed  ;  but  the  analogy  ceases  when  we  introduce 
a  foreign  resistance  opposing  such  velocity. 

In  discussing  the  flow  of  a  current  of  air  through  a 
mine,  we  are  dealing  with  a  fluid  medium  moved  or  ani- 
mated by  a  certain  pressure.  This  pressure  is  created 
and  maintained  by  the  resistance  ahead  of  the  current, 
upon  which  it  is  directly  dependent  and  not  upon  the 
power  behind  it.  This  is  a  very  important  distinction 
and  must  be  borne  in  mind  :  it  is  merely  stated  here, 
but  will  be  elucidated  further  on  in  the  growth  of  the 
subject.  It  is  aimed  in  this  chapter  to  refer  to  certain 


INTRODUCTION.  xiii 

facts  which  are  deduced  later,  in  order  to  prepare  the 
mind  for  a  systematic  study  of  the  subject. 

In  making  deductions  relative  to  the  fan,  the  method 
adopted  in  this  work  differs  essentially  from  the  method 
in  general  use,  but  seems  to  the  author  to  be  more  sim- 
ple and  practical.  It  is  based  upon  the  centrifugal  force 
developed  by  the  weight  of  air  revolved  by  the  fan- 
blades.  When  a  boy  ties  a  string  to  his  ball  and  swings 
it  about  his  head,  there  is  a  tension,  or  pull  upon  the 
string,  which  represents  the  centrifugal  force  developed. 
Applying  this  principle  to  the  fan,  the  air  contained 
between  the  blades  acts  as  the  ball ;  only  the  ball  pulls 
upon  the  string,  while  the  air  presses  outward  toward 
the  periphery  of  the  fan  and  creates  a  moving  or  ven- 
tilating pressure  in  the  mine.  The  blades  are  always 
full  and  the  air  is  revolved  by  them.  We  know  the 
weight  of  this  volume  of  air  in  revolution.  The  cen- 
trifugal force  developed  by  this  weight,  considered  as 
concentrated  at  the  centre  of  gravity  of  the  mass,  is 
easily  figured.  The  radial  force  thus  determined  is 
then  applied,  in  our  formulae,  to  each  particle  of  the  air 
in  question  (the  air  contained  between  the  blades),  on 
the  principle  that 

A  force  is  measured  by  the  velocity  it  can  generate  in  a 
unit  of  mass  in  a  unit  of  time. 

Thus,  by  combining  mass  of  air  with  radial  velocity, 
we  obtain  an  expression  (mv)  for  the  radial-mass-mot  ion, 
or  the  living  force  imparted  to  the  air  contained  between 
the  blades.  This  contained  air  has  then,  by  virtue  of 
its  revolution  in  the  fan,  been  transformed  into  a  radi- 
ally-moving mass,  whose  living  force  (mv)  is  the  power 
behind  the  current.  If  we  wish  to  determine  the  pres- 
sure the  fan  would  create  when  working  into  a  closed 


XIV  INTRODUCTION. 

space — or,  as  we  term  it,  the  "static"  pressure — we 
can  divide  the  force  developed  (mv)  by  the  surface 
pressed  (the  circumference  of  the  fan  multiplied  by  the 
width  of  blades).  This  is  not,  however,  the  most  im- 
portant determination  to  be  made.  It  is  more  impor- 
tant to  determine  the  work  of  this  centrifugal  force,  as 
indicated  by  the  expression  mv*,  which  is  the  force 
(mv)  multiplied  into  its  path  (v),  giving  the  work  for 
one  second  of  time.  This  will  give  us  the  work  any 
given  fan  can  accomplish  ;  and  taking  into  account  the 
coefficient  of  efficiency  (K),  we  place  the  effective  work 
of  the  fan  equal  to  the  work  to  be  accomplished  in  the 

Iks       \ 
mine  (  — <23 /•     In  this  method  we  deal  with  no  fiction, 

but  with  plain  facts  ;  and  we  believe  the  results  obtained 
are  simple  and  practical.  Work  must  always  be  placed 
against  work. 

This  brings  us  to  another  seeming  error  in  our  past 
formulas.  Mr.  Fairley  and  others  state  that,  "  If  we 
obtain  a  certain  quantity  of  air  by  the  action  of  a  fur- 
nace, and  another  certain  quantity  by  the  action  of  a  fan, 
or  other  means,  their  combined  effect  will  be  accord- 
ing to  the  square  root  of  the  sum  of  the  squares  of  the 
quantities  obtained  separately;  that  is,  according  to 
the  formula  Q  =  <J  q*  -\-q?.  Let  us  consider  a  moment. 
Suppose  our  furnace  acting  alone  will  pass  a  certain 
quantity  of  air  q,  and  our  fan  acting  alone  will  pass 
in  the  same  mine,  and  under  the  same  conditions,  a 
quantity  of  air  qr  Now,  the  work  the  furnace  will 
accomplish  is  denoted  by  the  equation 

ks    . 


INTRODUCTION.  XV 

and  likewise,  for  the  work  of  the  fan,  we  write 


But  the  combined  effect  must  be  equal  to  the  sum  of 
these  works,  as,  from  the  nature  of  the  hypothesis,  the 
work  performed  by  the  motors  in  the  two  instances  re- 
mains unchanged  ;  the  same  power  being  applied  to  the 
fan,  and  the  temperature  of  the  furnace  remaining  the 
same,  in  each  case.  Hence,  adding  equations  (a)  and 
(b),  member  to  member,  and  denoting  the  sum  of  the 
works  by  U,  we  have 


But  we  have 

-r  v  A/O     X~\3  /    1  \ 

U=—Q  .......    (d) 

Hence,    equating  the  values  of    U  as  given   by  equa- 
tions (c)  and  (d),  and  reducing,  we  have,  for  the  value 

of  Q,  

<2  =  •(¥+<?,'' 

which  is  very  essentially  different  from  the  expression 
in  general  use. 

It  is  a  fallacy,  in  discussing  the  mechanics  of  fluid's, 
to  suppose  that  if  one  motor  is  capable  of  yielding  a 
unit  of  pressure/,  and  another  motor  will  produce  a 
unit  of  pressure  p^ ,  working  under  the  same  condi- 
tions, their  combined  influence  will  yield  a  pressure 
equal  to  the  sum  of  these  respective  pressures.  This 
would  be  true  in  statics  (i.e.,  when  the  airways  are 


xvi  INTRODUCTION. 

closed  and  no  movement  results  from  the  pressure); 
but  in  dynamics  a  change  in  pressure  results  in  a 
change  of  velocity,  and  a  consequent  change  in  the  re- 
sistance of  the  airway,  which  last  again  affects  the 
pressure.  Consequently  the  only  basis  of  comparison 
is  by  means  of  the  work.  Statics  deals  with  pressure: 
dynamics  deals  with  work.  It  is  of  the  utmost  import- 
ance to  keep  this  in  mind  constantly,  in  treating  the 
subject  of  fluids. 

The  author  would  also  draw  particular  attention  to 
what  is  termed  in  the  following  pages  the   Potential 

factor  of  a  mine,f^TF=J,  and  also  its  equivalent  expres- 
sion, r=»  called  the  Potential  factor  of  ventilation. 


The  one  expression  gives  the  value  of  the  potential  in 
terms  of  the  mine  ;  the  other  gives  the  same  value  in 
terms  of  the  current.  The  potential  always  shows  the 
relation  existing,  in  a  certain  mine,  between  the  quan- 
tity of  air  passing  and  the  cube  root  of  the  power  neces- 
sary to  pass  such  quantity.  Thus,  denoting  the  po- 
tential factor  by  X,  we  have 


also, 


A  high  potential  always  indicates  a  well-ventilated 
mine,  as  it  shows  a  large  quantity  of  air  moved  by  a 
small  power.  It  is  obtained  by  increasing  the  area,  by 
splitting  the  air-current  \  also  by  decreasing  the  value 


INTRODUCTION.  xvii 

of  k  to  a  minimum,  by  cleaning  up  the  air-courses  and 
avoiding  sharp  bends  or  angles  as  far  as  possible. 

For  the  sake  of  illustration,  let  us  compare  two 
mines,  the  one  having  a  high  potential  factor,  as  mine 
No.  4,  with  three  splits  of  the  air-current  (see  Table 
X) ;  and  mine  No.  5,  having  but  a  single  current  of  air. 
This  latter  case  is  not  represented  in  the  tables.  At 
mine  No.  4  a  small  twelve-foot  fan,  blades  30  inches  wide, 
running  at  a  speed  of  60.8  revolutions  per  minute,  is 
throwing  50,000  cubic  feet  of  air,  against  a  potential  of 
647.344.  At  mine  No.  5>  when  there  is  but  a  single 
current,  the  potential  will  be  low,  viz.,  188.502.  Against 
this  potential,  a  twenty-foot  fan,  blades  48  inches  wide, 
running  at  a  speed  of  70.7  revolutions  per  minute,  will 
only  circulate  40,000  cubic  feet  of  air.  In  this  compari- 
son we  have  the  seeming  anomaly  of  a  twelve-foot  fan, 
making  only  60.8  revolutions  per  minute,  and  yielding 
50,000  cubic  feet  of  air,  while  our  twenty-foot  fan,  mak- 
ing 70.7  revolutions  per  minute,  is  yielding  but  40,000 
cubic  feet  of  air.  Many  casual  observers  would  at- 
tribute this  seeming  discrepancy  to  the  fan  and  say, 
"  The  fan  is  not  doing  its  share  of  work."  If,  however, 
we  glance  for  a  moment  at  the  work  being  performed 
in  each  case,  we  will  see  that  the  twenty-foot  fan  is 
accomplishing  a  work  of  289.546  horse-power,  while  the 
twelve-foot  fan  is  only  performing  a  work  of  13.963 
horse-power.  Hence  the  trouble  is  not  in  the  fan,  but 
in  the  method  of  ventilation  employed  in  the  mine. 

We  will  now  split  the  air  travelling  in  mine  No.  5, 
making  two  currents,  and  thereby  raising  the  mine 
potential  to  377.004.  We  find  now  that  the  power 
required  is  only  one  eighth  of  what  it  was  previously, 
and  our  small  twelve-foot  fan,  running  at  a  speed  of 


XV111  INTRODUCTION. 

797  revolutions  per  minute,  will  pass  the  same  amount 
of  air  as  was  passed  before  by  the  twenty-foot  fan. 
These  results  are  tabulated  below  and  serve  to  show 
the  importance  of  adopting  a  good  method  of  ventila- 
tion. The  fans  referred  to  in  each  case  are  the  fans 
described  in  Table  X  of  the  Appendix. 

Mine  No.  4.    Mine  No.  5.    Mine  No.  5. 

Quantity  passing . .  .      50,000        40,000        40,000 
Mine  potential 647.344       188.502       377.004 


No.  of  splits  

0 

I 

2 

Diameter  of  fan  

12  feet 

20  feet 

12  feet 

Width  of  blade.    .  .  . 

30  ins. 

48  ins. 

30  ins. 

Revs,  per  minute.  .  . 

60.8 

70.7 

797 

H.  P.  expended  

13-963 

289.546 

36.193 

Before  closing  this  introductory  chapter,  which  is  in- 
tended as  a  preliminary  sketch  of  the  ground  to  be 
gone  over,  the  author  would  state  that  the  tables  found 
in  the  Appendix  have  been  carefully  prepared  and  intro- 
duced, for  the  purpose  of  comparison,  and  to  show  at 
a  glance  results  under  varying  conditions.  It  must  not 
be  supposed  for  a  moment,  however,  that  because  any 
particular  fan  of  the  given  dimensions,  and  working 
seemingly  under  similar  conditions,  does  not  throw  the 
amount  of  air  indicated  in  the  table,  the  table  is  there- 
fore wrong:  there  are  many  agencies  of  ventilation 
constantly  at  work  in  the  pit,  and  these  all  have  their 
influence  upon  the  amount  of  air  passing.  To  eliminate 
these  secondary  influences,  and  obtain  a  simple  case  of 
fan  ventilation,  is  often  a  very  difficult  matter,  requir- 
ing patience,  care,  and  skill.  The  study  of  such  sec- 
ondary agencies  of  ventilation  will  be  taken  up  in 
detail  in  the  next  chapter. 


INTRODUCTION.  xix 

We  are  now  prepared  to  enter  upon  a  systematic  and 
thorough  study  of  our  subject,  beginning  at  the  rudi- 
ments which  the  student  must  become  a  thorough 
master  of  before  he  can  expect  to  grasp  the  more  in- 
tricate problems  with  which  the  subject  abounds.  We 
must  not  be  dazed  or  disheartened  because  of  the  com- 
plications which  arise  from  the  simultaneous  action  of 
so  many  agencies ;  but  the  student  must  bear  in  mind 
that  in  the  physical  world  every  law  continues  to  act 
just  as  though  no  other  law  existed.  Our  study  is 
throughout  a  study  of  those  God-given  laws  which 
energize  and  control  the  universe. 


TABLE   OF   CONTENTS. 


PAGE 

PREFACE v 

INTRODUCTION xi 

CHAPTER 

I.  CONDITIONS  EXISTING  IN  MINES i 

Ventilation.  Gases,  i.  Gaseous  and  Fiery  Mines — 
"  Blowers."  Kinds  of  Gases.  White  Damp,  2.  Black 
Damp,  3.  Fire-damp.  Resumt,  4.  Agency  of  the  Air- 
current.  Natural  Agencies  of  Ventilation,  5.  Sugges- 
tions. Natural  Ventilation,  6.  Illustration,  7. 

II.  FORCE  AS  APPLIED  TO  MINE-VENTILATION 8 

Prefatory.  Force,  8.  Measure  of  Force.  Static  Pressure. 
Dynamic  Pressure,  9.  Moving  Force  or  Ventilating  Press- 
ure. Natural  Pressure  :  How  it  obtains.  Weight  of  Air. 
Barometric  Pressure  :  Variations  in,  10.  Expression  for 
Weight  of  Air,  ir.  Effect  of  Temperature,  12.  Head-of-air- 
column.  Caution,  13.  Air-columns  as  Motors,  14.  Pressure 
in  Terms  of  Air-column,  15.  Primary-columns  and  Sec- 
ondary-columns, 16.  Three  Temperatures,  17.  Pressure 
in  Terms  of  the  Fan,  18.  Other  Motors.  Rfcumd,  20. 

III.  RESISTANCE  OF  THE  MINE 21 

Resistance.  Kinds  of  Resistance,  21.  How  Varies 
Static  Resistance.  Dips  and  Rises,  22.  Effect  upon  the  Cur- 
rent, 23.  Expression  for  Resistance.  Pressure  in  Terms 
of  the  Mine,  24.  Coefficient  of  Resistance.  Value  of,  25. 
Practical  Value  of  k.  Density  as  affecting  Resistance,  26. 

IV.  WORK 28 

Prefatory.       Definition     of    Work.       Unit    of     Work. 
Power.     Unit  of  Power,  28.     Horse-power.     Work  as  a 
Measure  of  Power.     Expression  for  Work,  29. 
V.  RESULTANT  FACTORS  OF  VENTILATION 31 

Resumd.      Prefatory.     Velocity.      Expressions   for   Ve- 


XX11  TABLE   OF   CONTENTS. 

CHAPTER  PAGE 

locity,  31.  Quantity.  Expressions  for  Quantity,  32.  Press- 
ure. Work.  Potential  Factor,  33.  Expression  for  the 
Potential  Factor.  Expressions  in  Terms  of  the  Potential, 
34,  Quantity  due  to  Two  Motors,  35.  Expression  for 
Head-of-air-column  in  Terms  of  Temperature  and  Motive- 
height.  Expression  for  Horse-power,  36.  Pressure  in 
Terms  of  Water-gauge.  Pressure  in  Terms  of  Temperature 
and  Motive-height,  37. 
VI.  EXPRESSION  FOR  STRAIGHT-PADDLE  FANS 38 

Prefatory.  Weight  of  Air  in  One  Section  of  the  Fan, 
38.  Centrifugal  Force  of  this  Weight.  Measure  of  this 
Centrifugal  Force,  39.  Work  of  the  Centrifugal  Force  per 
Second.  Work  of  the  Fan  per  Second,  40.  Effective  Work 
of  the  Fan  per  Minute.  Quantity  yielded  per  Minute  in 
Terms  of  the  Fan  and  Mine,  41.  Pressure  yielded  by  a 
Fan.  Horse-power  of  a  Fan,  42. 
VII.  ECONOMIC  DISCUSSION  OF  THE  FURNACE 43 

Prefatory.  Economic  Grate-area.  How  Determined, 
43.  Condition  of  Upcast  Current,  44.  Dry  Shafts.  Illus- 
tration, 45.  Wet  Shafts,  48.  Suggestions.  Relative  Quan- 
tities. Suggestions,  49.  Thermal  Unit.  French  Unit. 
American  Unit.  Calorics  of  Coals,  50.  Calorific  Capacity. 
Specific  Heat.  Specific  Heat  expresses  Thermal  Units. 
General  Expression  for  Weight  of  Coal,  51.  Gaseous  Com- 
position of  Upcast  Current,  52.  Expression  for  Weight 
of  Air  in  Terms  of  Q.  Expression  for  Weight  of  Ni- 
trogen. Expression  for  Weight  of  Carbonic  Acid  Gas,  53. 
Expression  for  Weight  of  Vapor  of  Saturation.  Summary. 
RJsum^  55.  Expression  for  Weight  of  Coal  to  heat  Air- 
current  (Dry  Shaft),  56. 
WET  SHAFTS 56 

Prefatory.      Condition  of  Shaft,    56.     Temperature   of 
Evaporation.     Absorption  of   Heat,   57,     Expression   for    * 
Extra  Coal  (Wet  Shaft),   58.      Cooling   Effect   of   Shafts. 
Expression  for  Coefficient  of  Cooling,  59. 
VIII.  ECONOMIC  DISCUSSION  OF  THE  FAN 62 

Prefatory.  Efficiency,  62.  Coefficient  of  Efficiency. 
How  varies,  63.  Internal  Resistance  of  a  Fan.  Work  of  the 
Resistance.  N.JB.  General  Expression  for  the  Work  of  the 
Fan,  64.  Value  of  K,  65  Relative  Efficiency  at  Differ- 


TABLE  OF  CONTENTS.  xxill 

CHAPTER  PAGE 

ent  Speeds.  Limit  of  Speed,  66.  Maximum  Effective 
Speed,  67.  To  determine  Value  of  K practically,  69.  Value 
of  the  Fan-constant.  Effect  of  Humidity,  70.  Rdsumt. 
Outer  Radius  or  Diameter,  72.  Inner  Radius  or  Size  of 
Eye.  Number  of  Blades.  Width  of  Blade,  73.  Curvature 
of  Blades,  74.  Expansion  of  Casing,  77.  General  Pro- 
portionment  of  the  Fan,  79.  Connection  with  the  Down- 
cast, 85.  Testing  a  Fan  at  the  Shops,  86. 
IX.  SPLITTING  THE  AIR-CURRENT 89 

Advantage  of  Splitting  as  shown  by  Table  VI.  Mines 
(assumed),  89.  Quantity  Increased.  Power  Decreased. 
Limit  to  Splitting,  90.  Size  of  Airways.  Arrangement  of 
Splits.  Equal  Splits,  91.  Unequal  Splits.  Natural  Divi- 
sion, 92.  Regulators,  93.  Present  Method,  94.  Objec- 
tion. Another  Method,  95.  Pro  and  Con.  Illustration, 
96.  Conclusion,  97. 
THE  THEORY  OF  SPLITTING  AIR-CURRENTS 98 

Dynamic  Equilibrium.  Theory  of  Splitting,  98.  Cau- 
tion. Graphic  Method,  99.  Style  of  Regulator  proposed, 
101.  Argument,  102.  Illustration,  103.  Objection,  104. 
System  in  Ventilation.  Effect  of  Dips  and  Rises,  106. 
Example,  107.  Cause  for  Disproportion,  108.  Effect 
tabulated,  109. 
X.  DISCUSSION  OF  THE  "  EQUIVALENT  ORIFICE  " no 

Prefatory.     Illustration,  no. 

XI.    COMPRESSIVE    VS.    EXHAUSTIVE    VENTILATION 115 

Prefatory.      Plenum    System.     Vacuum    System,     115. 
Difference.     Comparative  Effects,  116.     Conclusion,  119. 
XII.  CARE  OF  MINE  AS  ASSISTING  VENTILATION 121 

Prefatory.  Conduct  of  the  Air,  121.  Keep  Airways 
Clean.  Air  required  per  Minute  per  Man,  122.  Room- 
stoppings.  Entry-stoppings.  Break-throughs,  123.  Double- 
doors.  Overcasts.  Undercasts,  124.  Angles  in  Airways. 
Stables,  125. 


INDEX  TO  TABLES. 


I.  Comparison  of  the  Fahrenheit  and  Centigrade  Scales 128 

II.  Condition  of  the  Current  at  the  Bottom  of  Upcast 129 

III.  Tension  of  Aqueous  Vapor 130 

IV.  Specific  Heats  of  Various  Gases  and  Vapors 131 

V.  Specific  Gravity  of  Various  Gases  and  Vapors 131 

VI.  Effect  of  splitting  the  Air-current 132 

VII.  Horse-power  of  Different  Fans  at  Various  Speeds 133 

VIII.  Effect  of  Atmospheric  Changes  upon  the  Yield  of  a  Fan.  134-135 
IX.  Effect  of  Atmospheric  Changes  upon  the  Speed  of  a  Fan. .  136 
X.  Speed  and  Horse-power  of  Different  Fans  at  Different 

Mines 137-139 

xxv 


INDEX   TO    ILLUSTRATIONS. 


PAGE 

FIGURE. 

I.  Slope  or  Drift,  ventilated  by  a  Shaft 7 

II.  Illustration  of  a  Mine  (Ventilation  either  Natural  or  Arti- 
ficial), in  the  Ventilation  of  which  Three  Temperatures 
may  be  concerned I? 

III.  Represents  one  Section  of  a  Straight-paddle  Fan  ;  and  the 

Movement  of  the  Air-current  Relative  thereto 38 

IV.  Graphic  Representation  of  the  Curves  of  Efficiency  and  of 

the  Initial  and  Effective  Work  of  the  Fan,  with  Respect 

to  its  Speed 68 

V.  Cut  showing  a  Conical  Plate  surrounding  the  Fan-shaft, 

for  the  Purpose  of  deflecting  the  Intake-current  Radially.     75 
VI.  Sketch  showing  the  Arrangement  of  Blades  in  the  Murphy 

Fan 75 

VII.  Side  View  of  a  Fan  in  its  Casing,  showing  the  Peripheral 
Space  and  its  Connection  with  the  Downcast,  and  the 

Position  of  the  Cut-off 78 

VIII.  Sketch  showing  the  Method  of  testing  a  Fan  at  the  Shops.     87 

IX.   Illustration,  Tube  and  Water-gauge 96 

X.  Graphic  Method,  illustrating  the  splitting  of  the  Air-cur- 
rent    101 

XI.  Illustration  showing  a  Form  of  Regulator  that  will  propor- 
tion the  Power  applied  to  the  Mouth  of  any  Split  to  the 

Work  to  be  performed  in  that  Split 102 

XII.  Ideal  Plan  of  a  Mine,  worked  upon  the  Room  and  Pillar 
System  and  ventilated  in  Sections,  by  Means  of  Over- 
casts, avoiding  Doors  upon  the  Main  Hauling  Roads, 

and  employing  the  Improved  Form  of  Regulator 105 

XIII.   Illustration   of   the  "Vena   Contractor,"  referred    to    by 

Murgue  in  his  "  Equivalent  Orifice  "  Method no 

xxvii 


xxviii  INDEX   TO   ILLUSTRATIONS. 

FIGURE.  1'AGF 

XIV.   Illustration  showing  the  Fan-enclosure  and  Arrangement 

of  Doors  for  reversing  the  Air-current 119 

XV.   Illustration  showing  the  Location  of  an  Inside  Stable  in 

•    the  Entry-pillar  and  its  Ventilation  by  an  Air-leak 125 

XVI.   Illustration  showing  the  Location  of  an  Inside  Stable  on 
the  Side  of  the  Entry  and  its  Ventilation  by  an  Air-leak 

through  an  Overcast  Box 126 

XVII.  Illustration  showing  One  Section  of  a  Fan  having  Blades 
curved  Backward  from  the  Direction  of  Movement  and 
the  Reaction  of  the  Air  against  the  Surface  of  the  Blade 
(Addenda) 168 


€          OF  THE 
IVERSITX 
3 


MINE-VENTILATION. 


CHAPTER  I. 
CONDITIONS  EXISTING  IN  MINES. 

IT  is  essential,  before  entering  upon  a  discussion  of 
the  methods  and  means  of  ventilation  in  mines,  to  ob- 
tain and  hold  in  mind  a  clear  idea  of  the  elements  or 
factors  which  enter  into  and  form  the  component  parts 
of  our  problem. 

Ventilation. — First,  we  understand  by  the  term 
"  Ventilation,"  as  applied  to  mines,  the  removing  of  the 
air  contaminated  and  laden  with  the  poisonous  gases  of 
the  pit,  and  supplying  in  its  place  fresh  air  from  the 
outside.  To  do  this  requires  the  maintaining  of  a 
constant  current  of  air  through  the  pit,  and  conduct- 
ing such  current  by  means  of  doors,  stoppings,  over- 
casts, etc.,  around  the  entire  pit  and  particularly  to  the 
working  faces,  where  it  is  most  needed. 

Gases. — The  gases  occurring  in  the  pit  and  which 
contaminate  the  air  are  either  formed  in  the  mine,  first 
and  largely,  by  the  slow  combustion  of  coal  in  the  gob 
and  by  mine  fires  ;  second,  by  the  breathing  of  men  and 
aminals,  explosions  of  powder,  burning  of  lamps,  decay 
of  timber,  etc.,  giving  rise  for  the  most  part  to  the 
formation  of  carbonic  oxide  or  carbonic-acid  gas  ;  or, 


2  MINE-VENTILATION. 

as  is  the  case  with  hydrogen  carbide,  commonly  called 
Marsh-gas  or  Fire-damp,  they  exude  from  the  body  of 
the  coal,  as  a  product  of  earlier  formation. 

Gaseous  and  Fiery  Mines— "  Blowers."— Mines 
are  said  to  be  "  Gaseous  "  when  their  workings  emit 
natural  gases.  These  gases  may  issue  as  "  Blowers," 
under  pressure,  coming  from  some  internal  pocket, 
cavity,  or  chamber,  more  or  less  remote,  where  they 
have  accumulated  and  from  which  the}' escape  by  some 
crack,  crevice,  or  feeder  which  the  drills  may  have 
pierced,  or  a  settlement  in  the  mine  may  have  opened. 
When  these  natural  gases  are  combustible  or  explosive, 
the  mine  is  said  to  be  a  "Fiery"  mine.  In  such  mines 
the  question  of  ventilation  becomes  a  life-issue  and  the 
air-current  a  life-line.  Upon  the  constant  throb  and 
pulse  of  the  fan  depends  the  life  of  the  miner,  as  surely 
as  upon  the  beat  of  his  own  heart.  That  this  is  not 
true  in  non-fiery  mines  renders  such  mines  hardly  less 
dangerous  ;  because  the  consequent  partial  neglect  of 
the  question,  or  its  being  regarded  as  a  purely  second- 
ary matter,  renders  the  insidious  poisoning  from  mine 
gases  the  more  certain  and  deadly. 

Kinds  of  Gases. — The  gases  most  commonly  occur- 
ring in  mines  are  Carbonic-oxide  gas  (CO),  Carbonic- 
acid  gas  (CO2),  Marsh-gas  (CH4),  with  traces  of  Hydro- 
gen sulphide  (H,,S)  and  Ammonia  (NH3). 

"White  Damp." — Carbonic-oxide  gas  (CO),  com- 
monly called  "White  Damp,"  is  a  combustible  gas, 
burning  with  a  pale  blue  flame.  It  is  the  same  gas 
which  is  seen  burning  with  a  lambent  flame  over  a 
freshly-fed  anthracite  fire.  It  is  lighter  than  air,  hav- 
ing a  specific  gravity  of  0.967  and  hence  accumulates  in 
the  cavities  of  the  roof  and  in  the  upper  galleries  or 


CONDITIONS    EXISTING   IN   MINES.  3 

headings.  It  is  very  poisonous,  acting  as  a  narcotic. 
It  is  colorless  and,  in  the  mine,  odorless  and  therefore 
all  the  more  dangerous,  because  its  presence  may  escape 
the  notice  of  the  miner  until  too  late  for  him  to  avoid 
its  baneful  effects.  It  has,  however,  a  distinctly  sweet 
taste  in  the  mouth,  and  this  often  leads  to  its  detection. 
Its  effect  is  to  cause  a  stupor  or  drowsiness,  which  is 
often  followed  by  acute  pains  in  the  head,  back,  and 
limbs,  accompanied  with  delirium.  If  the  helpless  and 
unconscious  victim  is  not  rescued  soon,  death  is  the 
result.  The  gas  may  be  detected  in  the  mine  by  its 
effect  upon  the  flame  of  a  lamp,  causing  it  to  burn  with 
a  small  blue  tip  ;  and  when  present  in  any  considerable 
quantity,  the  flame  will  reach  upward  in  a  long  quiver- 
ing taper.  This  is  a  warning,  and  the  experienced 
miner  will  not  tarry  long  in  that  place,  as  he  knows  the 
danger  that  lurks  there.  This  gas  is  produced  by  the 
slow  combustion  of  coal  in  the  gob :  it  also  results 
from  mine  fires,  where  the  supply  of  air  is  scant;  and 
from  the  decay  of  vegetable  matter,  explosion  of 
powder,  etc. 

"  Black  Damp." — Carbonic-acid  gas  (CO2),  com- 
monly called  "  Black  Damp,"  is  an  incombustible  gas. 
It  is  heavier  than  air,  having  a  specific  gravity  of  1.529, 
and  hence  it  accumulates  in  the  swamps  and  the  low 
places  of  the  mine.  It  is  poisonous,  acting  as  a  nar- 
cotic, but  is  not  as  dangerous  a  gas  as  the  one  just  de- 
scribed, because  its  presence  is  more  readily  detected, 
from  the  dimness  of  the  lamps,  and  from  their  complete 
extinction  when  larger  quantities  of  the  gas  are  pres- 
ent. It  is  a  colorless  gas,  and,  in  the  mine,  has  very 
little  odor,  but  produces  a  sweet  taste  in  the  mouth. 
Its  effects  are  similar  to  those  of  carbonic-oxide  gas, 


4  MINE-VENTILATION. 

creating  also  headache  and  nausea.  It  is  produced  by 
active  combustion,  burning  of  lamps,  breathing  of  men 
and  animals,  decomposition  and  decay. 

"  Fire-damp." — Hydrogen  Carbide,  or,  as  it  is  com- 
monly called,  "  Marsh-gas,"  is  a  colorless,  odorless,  and 
tasteless  gas.  It  constitutes  the  well-known  "  Fire 
damp"  of  the  mines,  and  is  largely  responsible  for  the 
many  colliery  explosions  constantly  occurring.  It 
burns  with  a  slightly  luminous  flame  :  it  is  very  light, 
having  a  specific  gravity  of  only  0.559.  Like  hydro- 
gen it  is  combustible,  but  will  not  support  combustion 
when  pure  or  unmixed  with  air  or  oxygen.  This  gas 
mixed  with  3^  times  its  volume  of  air  will  not  explode  ; 
but  when  the  admixture  of  air  equals  5-^  times  the 
volume  of  the  gas  a  light  explosion  is  rendered  possi- 
ble ;  when  the  gas  is  mixed  with  9^  times  its  volume  of 
air  the  explosive  force  of  the  mixture  is  the  greatest ; 
the  presence  of  more  air  than  this  proportion  weakens 
the  explosive  force  of  the  mixture,  and  when  the  vol- 
ume of  the  air  equals  13  times  the  volume  of  the  gas 
the  explosion  is  again  very  weak.  The  Davy  lamp  is 
used  for  the  detection  of  this  gas  and  requires  great 
caution  and  watchfulness  to  insure  safety.  It  may  be 
detected  upon  the  lamp  until  the  admixture  of  air  has 
reached  about  50  volumes.  Marsh-gas  is  produced  by 
the  decay  of  vegetable  matter  under  water,  or  where 
the  air  has  been  wholly  excluded.  It  issues  from  coal- 
seams  probably  as  a  product  of  coal-formation,  where 
vegetable  matter  has  undergone  decomposition  through 
the  agency  of  heat  and  pressure,  with  the  entire  exclu- 
sion of  air. 

Resume. — We  have  now  considered  the  more  im- 
portant of  the  mine  gases.     The  remaining  gases  play 


XTNIVERSITTt 
CONDITIONS   EXISTINGN^N   MINUS. 

no  appreciable  part  in  the  consideration  of  the  subject 
of  mine-ventilation.  We  have  gone  over  in  detail  the 
natural  condition  of  a  pit ;  the  vitiating  influence  and 
the  poisonous  effect  of  its  exuding  gases ;  and  have  re- 
ferred to  the  general  method  in  use  for  removing  these 
gases,  viz.,  by  maintaining  a  constant  current  of  air 
through  the  pit. 

Agency  of  the  Air-current. — The  agency  of  the 
air-current  is  that  of  a  sort  of  common  carrier,  by 
which  the  g*ases  are  conveyed  out  of  the  mine.  This 
is  accomplished  through  the  action  of  the  laws  of  "  The 
Diffusion  of  Gases "  ;  the  obnoxious  and  poisonous 
gases  mixing  thoroughly  with  the  air  and  diffusing 
completely,  so  as  to  be  lost  in  the  current,  much  the 
same  as  a  drop  of  ink  becomes  lost  in  a  glass  of  water. 
Our  part  of  the  problem  then  becomes  the  maintaining 
of  a  constant  current  of  air  into  and  through  the  entire 
pit ;  relying  upon  the  working  of  natural  forces  for  the 
diffusion  and  extraction  of  the  gases. 

Natural  Agencies  of  Ventilation. — Before  taking 
up  the  study  of  the  applied  forces,  let  us  consider,  for 
a  moment,  what  natural  aids  or  hindrances  exist  in  the 
pit  which  become  active  forces,  either  aiding  or  oppos- 
ing the  circulation  of  the  air.  As  previously  stated,  in 
the  discussion  of  the  flow  of  air-currents,  we  are  dealing 
with  an  expansive,  fluid  medium,  moved  or  animated 
by  the  element  of  pressure.  Pressure  is  always  the 
expression  of  some  force  ;  or  obtains  when  a  force  is 
\vholly  or  in  part  arrested.  As  we  shall  see  in  the  next 
chapter,  in  the  study  of  applied  forces,  pressure  obtains 
as  a  ventilating  force  or  agency  whenever  two  columns 
of  air  in  equilibrium  have  different  temperatures. 
This  will  always  be  the  case  when  a  mine  is  ventilated 


6  MINE-VENTILATION. 

by  means  of  two  shafts,  an  upcast  and  a  downcast 
shaft ;  as  the  air-current  will  naturally  partake  of  the 
temperature  of  the  pit  through  which  it  passes.  Hence 
there  exists,  in  every  such  pit,  a  natural  agency  of  ven- 
tilation, either  aiding  or  opposing  the  applied  agencies 
in  their  work ;  and  the  influence  of  such  natural  agen- 
cies must  not  be  overlooked  in  careful  computations. 
This  same  natural  force  is  developed  in  entries  or  air- 
ways, running  to  the  rise  or  dip.  Such  rising  or  dip- 
ping entries  act  in  the  same  manner  as  shafts,  the 
vertical  height  through  which  they  rise  or  fall  being 
equivalent  to  the  depth  of  the  shaft.  The  action  of 
such  rise  or  dip  may  be  either  to  accelerate  or  retard 
the  circulation  of  the  pit. 

Suggestions. — On  account  of  the  above  existing 
forces  or  agencies,  we  should  always,  if  possible,  place 
the  fan,  when  forcing,  over  the  shorter  shaft,  making 
the  deeper  shaft  the  upcast  ;  for,  as  a  rule,  it  will  be 
the  warmer  of  the  two.  For  the  same  reason,  we 
should  always  endeavor  to  have  our  intakes  run  to  the 
dip  and  return  to  the  rise.  This  will  not,  however, 
always  be  found  possible  or  expedient.  When  we 
have  a  strongly-pitching  vein,  it  will  be  better  to  take 
the  air  in  at  the  lowest  point  and  discharge  it  at  the 
highest. 

Natural  Ventilation. — As  a  final  and  resulting  con- 
dition, existing  naturally  in  the  mine,  we  have  to  con- 
sider "  Natural  "  ventilation.  As  stated  above,  the  air- 
current,  or,  more  properly  speaking,  the  ventilating 
current,  is  animated  or  moved  through  the  element  of 
pressure.  When  this  animating  pressure  obtains  in 
the  pit  from  natural  causes,  it  gives  rise  to  natural  ven- 
tilation. Natural  ventilation  is  very  unreliable  and 


CONDITIONS   EXISTING   IN   MINES.  7 

changes,  as  regards  the  direction  of  the  current,  accord- 
ing to  the  relative  temperatures  of  the  outside  and 
inside  air. 

Illustration. — Fig.  I  represents  a  vertical  section 
through  a  drift,  connecting  with  an  air-shaft.  In  the 
winter  season  the  air  of  the  mine  will  be  warmer  than 
the  outside  air;  and  the  shaft  will  be  converted  into  an 
upcast  shaft,  the  intake  being  through  the  slope.  In 
the  summer  season  the  air  in  the  shaft  becomes  chilled 
and  heavier  than  the  outside  air  and  the  course  of  the 


Level  A 


FIG.  I. 

current  is  reversed.  Comparatively  very  few  mines 
rely  on  this  mode  of  ventilation,  but  all  are  subject  to 
its  influence  and  the  quantity  of  air  passing  in  every 
case  is  more  or  less  affected  by  it,  whatever  the  venti- 
lating motor.  It  is  important  that  this  should  be 
borne  in  mind  in  experimental  investigation. 


MINE-VENTILATION. 


CHAPTER  II. 

FORCE  AS  APPLIED  TO  MINE-VENTILATION. 

Prefatory. — Thus  far  we  have  taken  a  cursory  view 
of  the  natural  condition  of  the  pit :  we  have  looked 
over  the  ground  very  much  as  we  would  examine  a  new 
field  before  beginning  operations  relative  to  opening 
a  mine,  to  acquaint  ourselves  beforehand  with  its  exist- 
ing conditions,  the  work  to  be  done,  and  the  natural 
aids  and  hindrances  to  the  accomplishment  of  such 
work.  Let  us  now,  in  like  manner,  continue  to  exam- 
ine the  material  at  hand;  and  to  this  end  we  will  take 
up  the  study  of  force  as  applied  to  the  movement  of 
the  air-current. 

Force. — Force  is  an  abstract  idea :  we  cannot  see 
force  ;  we  can  only  see  its  results.  We  raise  a  hammer 
and  strike  a  blow  that  crushes  a  stone  :  we  do  not  see 
the  muscular  force  that  animated  the  blow ;  but  we  see 
its  effect,  which  is  the  demonstration  of  its  power.  We 
hold  in  our  hand  a  ten-pound  ball  and  we  feel  its 
weight,  or  we  place  it  in  the  scale-pan  and  see  it  de- 
flect the  beam  :  this  tangible  and  visible  effect  demon- 
strates to  us  the  existence  of  a  force  of  gravitation,  but 
we  do  not  see  the  force.  We  see  the  ship  flying  before 
the  wind  ;  we  feel  the  strength  of  the  hurricane ;  we 
see  the  devastation  of  the  tornado :  all  these  are  evi- 
dences of  a  force  behind  the  moving  air  which  ani- 
mates and  propels.  We  may  never  answer  the  question, 
"  What  is  force?"  ;  but  we  can  measure  and  compare 


FORCE   AS   APPLIED   TO    MINE-VENTILATION.          9 

force  with  force.  We  have  come  to  know  the  various 
transformations  of  force,  and  to  measure  it  according 
to  our  standards.  We  have  come  to  recognize  pressure, 
velocity,  heat,  etc.,  as  various  tangible  expressions  of 
force  ;  and  these  have  become  our  standards  of  measure. 

Measure  of  Force. — Force,  as  applied  to  air,  has 
three  measures,  according  to  the  conditions  under 
which  that  force  is  acting.  Let  us  suppose  that  we 
have  a  long  conduit  or  air-passage,  to  one  end  of  which 
we  apply  a  constant  force  by  means  of  a  fan  or  other 
motor;  three  conditions  may  obtain,  as  follows: 

1st.  Closed  conduit,  giving  pressure,  but  no  motion 
or  velocity. 

2d.  Long,  open  conduit,  giving  pressure  and  motion 
or  velocity. 

3d.  Short,  open  conduit,  giving  no  pressure,  but  ve- 
locity only,i 

Static  Pressure. — In  the  first  of  the  three  cases  just 
mentioned  the  force  is  converted  wholly  into  pressure  ; 
and  this  pressure,  called  the  "  Static  "  pressure,  is  the 
measure  of  the  force. 

Dynamic  Pressure. — In  the  second  of  these  cases 
the  force  is  converted  partly  into  pressure,  called  the 
"  Dynamic  "  pressure,  and  partly  into  velocity,  the  pres- 
sure and  the  velocity  bearing  an  inverse  ratio  to  each 
other  ;  i.e.,  as  the  pressure  increases,  the  velocity  de- 
creases and  vice  versa.  The  product  of  these  two  fac- 
tors is  the  measure  of  the  force  in  this  case. 

In  the  third  and  last  case  the  force  is  wholly  con- 
verted into  velocity.  If  this  velocity  could  be  measured, 
it  would  be  the  measure  of  the  force.  This  may,  how- 
ever, be  called  a  theoretical  case  with  respect  to  its 
application  to  mine-ventilation. 


10  MINE-VENTILATION. 

Moving    Force    or  Ventilating  Pressure. — The 

second  of  the  three  cases  just  referred  to  represents 
the  condition  which  obtains  in  the  mine.  The  moving 
force  or  pressure  under  which  the  air  is  moving  is  the 
power  behind  the  current,  and  which  animates  the  flow; 
it  is  the  total  pressure  exerted  against  the  sectional  area 
of  the  airway.  We  term  this  total  pressure,  in  this 
work,  the  "  Ventilating  "  pressure,  as  it  is  the  force  nec- 
essary to  move  the  current ;  or,  in  other  words,  the 
pressure  necessary  to  produce  ventilation.  The  unit  of 
pressure,  or  the  pressure  upon  one  square  foot  of  sec. 
tional  area,  we  term  the  "  Unit  "  of  ventilating  pressure. 
This  unit  of  ventilating  pressure  is  referred  to  by  Atkin- 
son, Fairley,  and  others,  as  the  ventilating  pressure, 
although  Mr.  Atkinson  tacitly  admits  that  such  method 
is  open  to  criticism.  We  represent  the  unit  of  venti- 
lating pressure  by  the  symbol  /,  and  the  ventilating 
pressure  itself  by  the  symbol  P  =  pa. 

Natural  Pressure :  How  it  Obtains. — Let  us  now 
investigate  how  the  element  of  pressure  obtains:  first, 
from  natural  causes,  and,  second,  by  the  application  of 
artificial  means,  such  as  the  fan  or  other  motor;  and 
afterward  find  expressions  for  such  pressure,  in  terms 
of  the  means  used. 

Weight  of  Air. — That  the  air  has  weight,  no  one  will 
deny.  It  may  be  shown  in  various  ways,  but  in  none 
more  simply  than  by  covering  one  end  of  a  short  tube 
or  cylinder  with  a  flexible  diaphragm,  and  exhausting 
the  air  from  the  tube  ;  the  diaphragm  will  be  pressed  in 
by  the  pressure  of  the  atmosphere  upon  it. 

Barometric  Pressure  :  Variations  In. — The  same 
pressure  is  also  shown  in  the  principle  of  the  barometer, 
where  the  atmosphere  supports  a  column  of  mercury 


FORCE   AS   APPLIED   TO   MINE-VENTILATION.        II 

which  varies  in  height  according  to  the  height  of  the 
observer  above  the  level  of  the  sea,  and  also  accord- 
ing to  the  state  of  the  atmosphere  at  the  time  of  the 
observation.  The  barometer  shows  the  pressure  due 
to  the  weight  of  the  atmosphere  to  be  subject  to  a 
slight  but  regular  diurnal  variation,  attaining  a  maxi- 
mum about  ten  o'clock  each  morning  and  evening,  and  a 
minimum  about  four  o'clock.  Besides  this  regular 
diurnal  variation,  there  is  also  shown  to  be  a  very 
irregular  fluctuation  in  the  atmospheric  pressure,  accord- 
ing to  the  presence  of  storm-centres,  and  according  to 
the  amount  of  moisture  in  the  air,  or,  as  we  say,  its 
hygrometric  state  ;  and  other  causes  not  necessary  to 
mention  here.  But,  disregarding  these  fluctuations  for 
the  present  purpose,  the  pressure  of  the  atmosphere  at 
any  level,  or  the  barometric  pressure,  is  produced  by 
the  weight  of  the  air  above  that  level,  which  fact  plays 
a  very  important  part  in  our  discussion. 

Expression  for  Weight  of  Air. — Our  problem  is  to 
find  an  expression  for  the  weight  of  a  unit  of  volume 
of  dry  air  at  any  temperature  (/°),  and  under  any  bar- 
ometric pressure  (Bff).  Ganot,  in  his  "  Elements  de 
Physique,"  gives  as  the  result  of  careful  experiments 
the  weight  of  100  cubic  inches  of  dry  air  at  the  tem- 
perature of  1 6°  C.  and  a  barometric  pressure  of  30",  to 
be  31  grains.  This  reduced  gives,  as  the  corresponding 
weight  of  one  cubic  foot  of  dry  air,  at  a  temperature  of 
o°  F.  and  a  single  inch  of  barometer,  0.0028885  pounds 
avoirdupois,  which  agrees  very  closely  with  the  results 
given  by  Atkinson.  It  has  further  been  ascertained  by 
careful  experiment  that  air  will  expand  ^-J-g-  of  its  vol- 
ume for  each  degree  of  temperature  of  the  Fahrenheit 
scale ;  and  hence,  taking  the  volume  at  o°  F.  as  one, 


12  MINE-VENTILATION. 


the  volume  at  any  temperature,  as  /°,  will  be  I  + 

459  ' 
and  the  weights  per  cubic  foot  being  inversely  propor- 

tional to  the  volumes,  we  have 

I  :  I  H  --  ::w:  .0028885  ; 

459 
hence 


459  X  .0028885 


or 


w  being  the  weight  of  one  cubic  foot  of  dry  air  at 
t°  and  \"  barom.  Now  as  the  weights  of  equal  vol- 
umes are  proportional  to  the  barometric  pressures,  and 
for  the  sake  of  uniformity  adopting  Mr.  Atkinson's 
figure,  we  have  finally,  for  the  weight  of  one  cubic  foot 
of  dry  air  at  a  temperature  of  f  and  under  a  baro- 
metric pressure  of  B", 


459 


Effect  of  Temperature.  —  We  come  now  to  realize 
that  the  atmosphere  about  us  has  weight,  and  that  this 
weight  is  a  considerable  pressure.  We  see  from  equa- 
tion (I),  that  the  weight  of  air  is  dependent  upon  the 
temperature,  and  that  it  varies  inversely  as  the  expres- 
sion 459  -|-  t.  Therefore,  if  two  columns  of  air,  as,  for 
example,  two  shafts  connected  by  the  airways  of  a 
mine,  have  different  temperatures,  they  will  not  main- 
tain a  static  equilibrium,  but  a  moving  pressure  will  be 


FORCE   AS  APPLIED   TO    MINE-VENTILATION.        13 

developed,  incident  to  the  two  temperatures;  and  this 
surplus  pressure  is  the  moving  or  ventilating  pressure 
spoken  of  previously. 

Temperature,  then,  is  directly  responsible  for  natural 
pressure  as  it  obtains  in  the  mine. 

"  Head-of-air  Column. " — It  has  been  found  conven- 
ient to  express  the  unit  of  ventilating  pressure  in  terms 
of  "  Head-of-air  Column,"  so  called,  representing  the 
pressure,  from  whatever  source,  as  though  animated  by 
the  weight  of  such  column  of  air.  This  head-of-air 
column  is  sometimes  called  the  "  Motive  Column."  It 
is  an  imaginary  column  of  air  of  such  height  as  to  pro- 
duce by  its  weight  the  pressure  required.  Denoting 
this  head-of-air  column  by  H ",  its  value  will  be  ex- 
pressed by  the  equation 

X459  +  0  /IF) 

- 1.3253  x*' 

Caution. — In  using  this  imaginary  motive-column 
we  must  not  for  a  moment  suppose  that  the  velocity  of 
the  air  in  the  mine,  due  to  this  pressure  represented,  is 
the  same  as  the  velocity  generated  by  a  body  falling 
through  the  height  H '.  This  is  an  error  made  by 
many,  and  we  cannot  be  too  careful  in  its  avoidance. 
We  would  refer  back  to  what  has  already  been  said  in 
reference  to  this  in  the  introductory  chaptefv  Were 
there  no  resistance  ahead  of  the  current,  or,  in  other 
words,  were  the  power  converted  wholly  into  velocity, 
this  supposition  would  be  correct  ;  but  this  is  not  the 
case.  We  are  dealing  in  this  instance  with  movement 
under  pressure,  or,  as  we  say,  a  dynamic  pressure. 
We  assume  the  power  applied  to  be  sufficient  to  give 


14  MINE-VENTILATION. 

a  certain  quantity  in  a  certain  mine  ;  that  is  to  say,  a 
certain  velocity  under  a  certain  water-gauge  or  pres- 
sure. Now  it  is  to  the  power  that  we  look  fo-r  the  pro- 
duction of  the  velocity,  whatever  the  opposing  pressure. 
The  pressure  exists  by  virtue  of  the  dynamic  resistance  ; 
and  the  resistance  depends  not  alone  upon  velocity, 
but  upon  another  variable  factor,  viz.,  the  rubbing 
surface  of  the  airways.  It  is  true  that  the  head-of-air 
column  or  motive  column  is  representative  of  a  pres- 
sure, but  such  pressure  is  not  analogous  to  the  dynamic 
pressure  of  the  air-current,  for  the  reason  that  it  is  not 
governed  by  the  same  laws,  We  may  have  in  two  dif- 
ferent mines,  whose  airways  have  the  same  sectional 
area,  the  same  head-of-air  column,  as  representative  of 
the  same  ventilating  pressure,  and  yet  yielding  differ- 
ent velocities  and  quantities,  according  as  the  rubbing 
surfaces  in  those  two  mines  are  different.  It  is  the  re- 
sistance that  creates  and  maintains  the  dynamic  pres- 
sure. This  will  be  more  readily  seen  in  the  study  of 
the  next  chapter. 

Head-of-air  Column,  or  pressure  as  applied  to  the 
movement  of  fluids,  and  Generative  Height,  as  applied 
to  falling  bodies,  are  not  correlative  terms. 

Air-columns  as  Motors. — Let  us  refer  again  to  Fig. 
I  and  assume  two  imaginary  vertical  columns  of  air, 
having  their  bases  at  B'  and  B" ,  respectively,  and  ex- 
tending upward  through  the  atmosphere.  If  we  assume 
these  imaginary  air-columns  to  have  each  a  base  of  one 
square  foot  area,  the  weight  of  air  in  each  column 
above  any  level,  as  level  A  or  level  B,  will  be  the  unit 
of  pressure  at  such  point.  Multiplying  this  unit  of 
pressure  by  the  sectional  area  of  the  airway,  we  obtain 
the  total  pressure  upon  the  air  at  level  B  due  to  the 


FORCE  AS   APPLIED   TO    MINE-VENTILATION.        I  5 

weight  of  the  air  above.  These  two  imaginary  columns 
of  air,  when  connected  below  by  airways,  will  be 
in  equilibrium — static  equilibrium  if  their  weights  are 
equal,  when  no  current  will  result  ;  and  dynamic  equilib- 
rium if  their  weights  are  unequal  and  a  current  estab- 
lished. It  is  evident  now  that  the  weights  of  the  two 
columns  of  air  above  level  A  will  always  be  the  same, 
being  subject  to  the  same  temperature,  and  therefore 
may  be  ignored  in  ascertaining  the  differential  pres- 
sure. Below  this  level  they  may  be  very  different. 
This  difference  of  temperature  may  result  either  from 
natural  causes,  as  the  heat  of  the  mine,  or  from  the  ap- 
plication of  artificial  means,  as  the  heat  of  a  furnace. 
In  either  case  a  difference  of  pressure  will  result,  and 
the  air  in  the  airways  will  be  urged  to  move  from  the 
point  of  greater  pressure  to  the  point  where  the  pres- 
sure is  less,  the  moving  force  being  the  surplus  of  pres- 
sure which  we  term  the  ventilating  pressure. 

Pressure  in  Terms  of  Air-column. — The  vertical 
height  h  between  level  A  and  level  B,  Fig.  I,  we  will 
call  the  "  Motive  Height,"  because  it  is  the  height 
through  which  the  motive  force  is  exercised  or  devel- 
oped, but  this  term  must  not  be  confounded  with  the 
term  motive  column,  or  head-of-air  column  previously 
referred  to,  as  its  significance  is  widely  different.  In 
ascertaining  the  differential  or  moving  pressure,  we  are 
concerned  only  with  the  motive  height. 

Assume  the  following: 

t  —  temperature  of  the  outer  air; 
/,  —  avg.  temp,  of  the  air  in  the  upcast  shaft ; 
w  =  wt.  of  one  cu.  ft.  of  the  outer  air ; 
wl=    "    "     "      "     ""     "     air  in  the  upcast  shaft; 
B  =  height  of  the  barometer  in  inches  ; 


1  6  MINE-VENTILATION. 

h  =  motive  height  ; 

a  =  area  of  cross-section  of  the  airway. 
Then 

(w  —  w^  —  the  differential  unit  of  weight  ; 
h(w  —  w^—    "  "  "     "     pressure; 

ah(w—w^  —  P  —  the  moving  or  ventilating  pressure. 
Referring  to  equation  (I),  we  have 


459  +  ' 
and 

1^25320? 

' 


..    (HI) 


When  /,  is  greater  than  /,  the  value  of  P  will  be 
positive,  which  indicates  an  upcast  current  in  the  shaft  ; 
when  /j  is  less  than  /,  the  value  of  P  becomes  nega- 
tive, and  then  indicates  a  downcast  current  in  the 
shaft.  Equation  (III)  is  true  for  all  cases  of  mine-ven- 
tilation where  only  two  temperatures  are  concerned  in 
producing  pressure.  This  is  the  case  in  a  slope  or  drift- 
mine  ventilated  by  a  shaft,  either  by  natural  draught 
or  by  a  furnace  ;  also  in  a  mine  ventilated  by  means  of 
two  shafts,  where  either  the  downcast  shaft  is  so  shal- 
low as  to  have  practically  the  same  temperature  as  the 
outer  air,  or  the  mouths  of  the  two  shafts  are  on  the 
same  level. 

Primary  Columns  and  Secondary  Columns.  —  In 
all  cases  of  natural  ventilation  the  deeper  shaft  will  de- 
termine the  course  of  the  current,  by  its  relative  tern- 


1ORCE  AS   APPLIED   TO    MINE-VENTILATION.        \J 

perature  ;  in  all  cases  of  furnace-ventilation,  the  fur- 
nace shaft  will  determine  the  course  of  the  current, 
being  the  upcast.  Therefore  we  may  call  these  shafts 
the  "Primary  Columns"  and  the  other  shafts  the 
"  Secondary  Columns."  The  temperature  of  the  pri- 
mary column  is  always  represented  by  one  temperature, 
while  the  secondary  column  may  possess  two  separate 
and  distinct  temperatures,  which  cannot  be  averaged 
accurately.  This  gives  rise  to  a  case  of  mine-ventila- 
tion where  three  temperatures  are  concerned  in  pro- 
ducing the  ventilating  pressure. 

Three  Temperatures.— Fig.  II  illustrates  a  case  of 
mine-ventilation  (either  natural  or  by  a  furnace),  where 
three  temperatures  may  be  concerned. 


'///////////////////^/Z^W/JW///;^^ 

FIG.   ii. 


Assume  the  following: 

dl  =  depth  of  the  primary  or  deeper  shaft 
d  =  depth  of  the  secondary  shaft ; 


J8  MINE-VENTILATION. 

(dl  —  d)  =  height  of  the  outer  effective  column  ; 
tl  =  avg.  temp,  of  the  primary  shaft  ; 
/2  =  avg.  temp,  of  the  secondary  shaft  ; 
t  —  temp,  of  the  outer  air. 

Then,  by  applying  the  same  method  used  to  obtain 
equation  (III),  we  have 


Equations  (III)  and  (IV)  will  cover  all  cases  of  natu- 
ral and  furnace  ventilation  that  will  arise,  and  express 
in  pounds  avoirdupois  the  value  of  the  elementary 
pressure  due  to  heated  air-columns. 

Pressure  in  Terms  of  the  Fan.  —  We  will  now  de- 
termine the  pressure  due  to  the  action  of  a  fan.  For 
the  present  we  will  content  ourselves  with  determining 
the  static  pressure  the  fan  is  capable  of  yielding,  i.e., 
the  pressure  the  fan  would  give  if  working  into  a  closed 
space.  In  all  cases  of  compressive  ventilation  the  pres- 
sure is  created  and  maintained  by  the  resistance  of  the 
mine,  and  its  value  is  expressed  in  terms  of  the  mine  ; 
and  for  this  reason  we  delay  its  discussion  till  later. 
The  method  here  adopted  for  determining  the  static 
pressure  due  to  the  action  of  the  fan  depends,  as  pre- 
viously stated,  upon  the  centrifugal  force  developed  by 
the  mechanical  revolution  of  the  air  contained  between 
the  blades  of  the  fan.  This  contained  air  possesses  a 
certain  weight,  and  this  weight  of  air,  compelled  to  re- 
volve at  a  certain  speed  by  virtue  of  its  mechanical 
environment,  will  develop  a  certain  centrifugal  force  or 
outward  pressure. 

Assume  the  following: 


FORCE   AS   APPLIED   TO   MINE-VENTILATION.        1  9 

R  —  outer  radius  of  the  fan-blades; 
Rl  =  inner  radius  of  the  fan-blades  ; 

b  =  breadth  of  blades  ; 

TZ,  =  number  of  blades  ; 

n  =  number  of  revolutions  per  minute; 
R^  =  rad.  of  the  cen.  of  grav.  of  one  compartment; 

v^  —  vel.  of  the  cen.  of  grav.  of  one  compartment  ; 

z\  =  capacity  between  two  consecutive  blades  ; 

W  '  =-  wt.  of  air  between  two  consecutive  blades; 

F  =  centrif.  force  of  air  in  one  compartment; 

g—  acceleration  due  to  gravity  (32.19); 

p  =  unit  of  pressure; 
/  =  temperature  of  the  air  ; 

B  =  barometric  pressure  in  inches  ; 
Now,  since  the  unit  of  pressure  is  equal  to  the  entire 
centrifugal   force   developed  in    all  the   compartments 
divided  by  the  surface  pressed,  we  write 


From  mechanics,  we  have 


<•> 


But  as  v^  is  the  velocity  of  the  centre  of  gravity  of 
one  compartment,  in  feet  per  second,  to  correspond  to 
the  value  of  g,  which  is  in  feet  per  second,  we  have 


(3) 


and,  from  mechanics,  we  have  for  the  value  of 


2O  MINE-VENTILATION. 

We  have   also,  from  equation  (I),   remembering  that 
W  —  wvl  , 


Also,  from  geometry,  we  have 

,,  =  ^^  .....     (6) 

Finally,  by  combining  these  six  elementary  equations 
and  reducing,  we  have 

/  =  0.0001  So5«.(*  -RR^x—f    .     .   (V) 


Equation  (V)  is  applicable  to  all  straight  paddle-fans, 
and  expresses,  in  pounds  avoirdupois,  the  unit  of  static 
pressure  the  fan  is  capable  of  producing. 

Other  Motors.  —  Other  air-motors  are  the  steam-jet, 
waterfall,  and  various  kinds  of  screw  machines  and 
volumetric  appliances;  but  these  are  all  unscientific, 
and  are  rapidly  falling  into  disuse.  They  will  not  be 
discussed  in  this  work. 

Resume.  —  We  have  now  referred  to  pressure  as  de- 
veloped by  and  expressed  in  terms  of  some  motor,  or, 
in  other  words,  as  the  representative  or  agent  of  some 
animating,  energizing  force.  The  following  chapter 
will  consider  opposing  pressure  as  expressed  in  terms  of 
the  resistance  of  the  mine. 


RESISTANCE   OF  THE   MINE.  21 


CHAPTER  III. 

RESISTANCE  OF  THE  MINE. 

Resistance.  —  By  Resistance,  in  general,  is  meant  the 
force  opposed  to  the  movement  of  a  body.  -  It  is  always 
opposed  to  the  moving  force.  Resistance  to  the  move- 
ment of  a  fluid  always  creates  a  pressure  throughout 
its  mass,  and  this  pressure  is  one  of  the  factors  by 
which  we  measure  the  moving  force  applied,  as  we  shall 
see  in  the  next  chapter.  In  the  case  of  the  flow  of  air 
through  the  airways  of  a  mine,  the  resistance  (which 
is  due  to  the  rubbing  of  the  air-current  along  the  sides, 
roof,  and  floor  of  the  airway)  is  applied  all  along  the 
entire  length  of  the  current.  For  this  reason  the 
pressure  arising  therefrom  decreases  as  we  proceed 
along  the  airway  and  approach  the  discharge,  where  it 
is  nil.  From  a  consideration  of  this  last  fact  we  readily 
see  that  the  ventilating  pressure  in  a  mine  can  never 
be  greater  than,  but  is  always  equal  to,  the  resistance 
offered  by  the  mine  to  the  passing  of  the  current.  This 
resistance  has  been  improperly  called  the  "  Drag"  of 
the  mine.  There  is  no  drag  or  pull  known  in  the  study 
of  physical  laws  relating  to  fluids.  Force  or  power  is 
always  behind  the  opposing  resistance. 

Kinds  of  Resistance.  —  It  is  well  to  notice  that  re- 
sistance is  of  two  kinds.  What  we  will  call  the  "  Static  " 
resistance  or  the  force  to  be  overcome  in  order  to  cre- 
ate  a  circulating  current,  fs  much  greater  than  the 
"  Dynamic  "  resistance,  or  the 


OF  THE 


22  MINE-VENTILATION. 

maintaining  such  current  after  it  is  established.  What 
will  interest  us  the  most  in  the  study  of  the  following 
pages  is  the  dynamic  resistance,  and,  as  stated  above, 
it  is  equal  to  the  ventilating  pressure  pa. 

How  Varies. — The  dynamic  resistance  varies  theo- 
retically as  the  extent  of  the  rubbing  surface  and  as  the 
square  of  the  velocity  of  the  current.  This  is  what  we 
would  naturally  expect,  because,  if  the  velocity  of  the 
air-current  be  doubled,  each  particle  of  air  strikes,  in  a 
unit  of  time,  twice  the  amount  of  resistance,  and  each 
opposing  blow  is  of  twice  the  force  ;  therefore  the 
resistance  is  as  the  square  of  the  velocity  of  the  current ; 
and  as  the  number  of  resisting  particles  increases  with 
the  rubbing  surface,  the  resistance  will  increase  in  the 
same  ratio.  We  say  the  resistance  varies  theoretically 
as  the  extent  of  the  rubbing  surface,  but,  practically, 
the  physical  condition  of  the  surface  rubbed,  as  being 
rough  or  smooth,  will  vary  the  amount  of  the  resist- 
ance ;  also,  there  can  scarcely  be  a  doubt  but  that  the 
moisture  condensed  upon  the  sides  and  roof  of  the  air- 
way will  act  as  a  lubricant,  and  thereby  reduce  the 
resistance.  Sharp  bends  or  projecting  angles  in  the 
airway  are  a  serious  hindrance  to  the  passage  of  the 
air,  and  largely  increase  the  resistance.  But  all  of  these 
are  physical  causes,  affecting  the  coefficient  of  friction 
to  be  referred  to  hereafter ;  they  in  no  way  affect  the 
working  of  the  law  by  which  resistance  varies,  and  given 
above. 

Static  Resistance.  —  Static  resistance  cannot  be 
formulated,  as  it  depends  upon  too  many  arbitrary 
conditions  and  influences.  When  resistance  is  spoken 
of  in  this  book  it  is  dynamic  resistance  which  is  meant. 

Dips   and   Rises. — An    important    factor   affecting 


RESISTANCE   OF  THE   MINE.  23 

the  flow  of  the  air-current,  and  which  is  often  alluded 
to  as  a  resistance  (but  it  is  not  a  resistance,  properly 
speaking),  is  the  occurrence  in  the  entries  or  airways 
of  dips  or  rises.  The  effect  of  such  dips  or  rises,  as 
aiding  or  retarding  the  flow  of  the  air,  will  be  discussed 
in  this  chapter ;  the  question  of  such  dips  and  rises 
affecting  the  proportionate  flow  at  different  velocities 
will  come  up  for  discussion  in  the  chapter  upon  "  Split- 
ting the  Air"  (Chapter  IX). 

Effect  upon  the  Current. — Considerable  diversity 
of  opinion  has  always  existed  among  miners  regarding 
the  effect  of  a  dip  or  a  rise  in  the  entry.  It  may  be 
said  with  reason,  however,  that  an  intake  working  to 
the  dip  will  assist  ventilation,  while  an  intake  working 
to  the  rise  will  retard  the  same.  This  has  been  demon- 
strated a  number  of  times:  it  will  only  be  found  to 
fail  when  the  intake  is  warmer  than  the  return,  which 
is  seldom.  The  reason  is  obvious,  and  has  already  been 
referred  to  in  the  discussion  of  "  Natural  Agencies  of 
Ventilation  "  (Chapter  I).  If  an  air-course  works  to 
the  dip,  its  return  must  show  an  equal  rise  in  vertical 
height.  This  is  evidently  true  whether  the  return  par- 
allels the  air-course  or  not,  except  in  some  special 
ca^es — as,  for  example,  a  tunnel  having  two  openings, 
or  some  similar  instance  of  one  direct  current  and  no 
return.  A  mine  in  which  the  upcast  shaft  is  located  at 
a  considerable  distance  from  the  downcast  is  an  exam- 
ple of  one  direct  current.  An  intake  running  to  the 
dip  and  its  return  to  the  rise  is  but  an  illustration  of 
natural  ventilation  in  the  large  majority  of  cases,  as 
the  warmer  air  of  the  pit  will  naturally  tend  to  rise, 
while  the  cool  outer  air  likewise  descends  to  take  its 
place.  On  the  other  hand,  an  intake  running  to  the 


24  MINE-VENTILATION. 

rise  and  its  return  to  the  dip  presents  a  condition  of 
things  which  is  contrary  to  the  natural ;  and  a  venti- 
lating current  compelled  to  travel  in  that  direction 
will  have  this  natural  force  or  agency  to  overcome. 
The  influence  of  dips  and  rises  is  a  very  potential  one  ; 
its  potentiality  depending  upon  the  vertical  height  of 
the  dip  or  rise  and  the  differential  temperature  of  the 
intake  and  the  return.  It  is,  as  we  have  said,  another 
case  of  natural  ventilation,  in  which  the  vertical  height 
of  the  rise  or  dip  corresponds  to  the  motive  height  h 
of  equation  (II).  The  influence  of  dips  and  rises  as  a 
ventilating  power  must  always  be  taken  into  account 
in  nice  calculations  upon  mining  problems,  especially 
in  figuring  upon  the  proportionment  of  air  in  different 
splits,  and  when  the  amount  of  the  dip  or  rise  is  con- 
siderable. 

Expression  for  Resistance. — In  obtaining  an   ex- 
pression for  the  resistance  offered  by  a  certain  mine  to 
its  ventilating  current  we  assume  the  following: 
R  =  dynamic    resistance,   opposed   to  any   ventilating 

pressure  P  =  pa  \ 

v  =  velocity  of  the  air-current  in  feet  per  minute  ; 
s  =  rubbing  surface  of  the  entries  or  airways  exposed 

to  the  current,  expressed  in  square  feet ; 
k  =  unit  of  resistance,  or  the  resistance,  expressed  in 

pounds  (avoir.),  offered  by   I   sq.   ft.  of  rubbing 

surface  to  air  moving  with  a  velocity  .of  I  ft.  per 

minute. 
Then  we  may  write,  from  what  has  preceded, 

R  =  ksv* (VI) 

Pressure  in  Terms  of  the  Mine. — From  what  has 


RESISTANCE   OF  THE    MINE.  25 

preceded  we  have  also  seen  that  the  ventilating  pres- 
sure P  =  pa  is  opposed  and  equal  to  the  resistance  R\ 
hence  we  may  also  write 


(VII) 


Then,  by  substituting  this  value  of  R  in  equation  (VI), 
and  solving  with  respect  to  p,  we  have 


Coefficient  of  Resistance. — What  we  call  the  "  Co- 
efficient "  of  resistance  is  really  the  unit  of  resistance  ; 
it  is  expressed  in  our  formulas  by  the  symbol  k. 
Solving  equation  (VIII)  with  respect  to  k,  we  have 

k=&  (IX) 

SV*  ^  •     } 

Value  of. — On  account  of  the  various  obstructions 
in  the  airways,  and  the  varying  physical  conditions  of 
the  mine  and  airways,  referred  to  in  the  early  part  of 
this  chapter,  no  two  mines  will  give  exactly  the  same 
value  for  k.  The  value  of  /£,  as  deduced  by  Mr. 
Atkinson,  from  a  large  number  of  experiments  by 
others,  has  been  very  generally  adopted  ;  and  we  see 
no  good  reason  for  changing  it,  except  it  may  be  in 
some  particular  determination.  For  the  purposes  of 
general  calculation  and  for  the  sake  of  uniformity,  it 
should  be  always  used.  This  value,  as  given  by  Mr. 
Atkinson,  is 

k  =  0.9000000217. 

The  method  of  mining,  mode  of  timbering,  and  other 


26  MINE- VENTILATION. 

details  of  working,  which  vary  considerably  according 
to  the  customs  habitual  in  the  district  wherein  the 
mine  is  located,  may  give  upon  investigation  a  coeffi- 
cient more  adapted  to  the  mines  in  that  district.  Such 
a  local  value  of  k  may  be  determined  by  taking  care- 
ful observations  in  several  typical  mines  of  that  dis- 
trict and  then  averaging  the  results,  avoiding  any  that 
might  seem  to  be  unreliable  on  account  of  obstructed 
airways,  small  break-throughs,  or  other  similar  defects. 

Practical  Value  of  k. — The  practical  benefit  aris- 
ing from  a  known  local  value  of  k  would  be  the  ascer- 
taining therefrom  the  necessary  ventilating  pressure 
for  any  proposed  workings,  in  estimating  and  decid- 
ing upon  size  of  fans  and  power  of  engines  to  be  em- 
ployed. It  is  a  good  factor  to  know  ;  and  after  its 
value  has  been  established  in  any  district  or  class  of 
workings,  by  careful  observations  in  mines  that  are 
well  kept,  its  subsequent  application  to  other  mines  in 
that  district  will  show  the  comparative  condition  of 
the  air-courses  in  such  mines. 

Density  as  affecting  Resistance. — The  question  is 
often  asked,  "  Does  a  change  in  the  density  of  the  flow- 
ing air  affect  in  any  way  the  resistance  or  the  power?  " 
As  far  as  the  resistance  offered  by  the  mine  to  the  pass- 
ing current  is  concerned,  the  density  of  the  flowing  air 
does  not  change  sufficiently  to  produce  any  appreciable 
effect.  Likewise,  also,  the  power  is  not  appreciably 
affected  as  far  as  the  mine  is  concerned — that  is  to  say, 
the  power  required  to  pass  a  certain  quantity  of  air  per 
minute  through  that  mine.  But,  on  the  other  hand, 
the  efficiency  and  power  of  the  fan  is  very  seriously 
affected  by  changes  in  the  density  of  the  air.  This 
part  of  the  subject,  however,  will  be  discussed  later — 


RESISTANCE   OF   THE    MINE.  2/ 

Chapter  VIII.  The  causes  which  give  rise  to  a  change 
of  density  in  the  air  of  the  pit  are  very  numerous: 
first,  the  pressure  of  the  pit  due  to  the  resistance  (this 
pressure  decreases  all  the  way  along  the  current,  from 
the  intake  to  the  discharge,  and  affects  the  density 
correspondingly);  second,  the  heat  of  the  mine  which 
is  more  potent  in  its  effect;  third,  the  absorption  of 
aqueous  vapor  by  the  air  in  its  passage  through  the 
pit ;  the  density  of  the  air  being  very  slightly  dimin- 
ished by  this  absorption.  The  return  current  is  always 
saturated,  or  carrying  as  much  moisture  as  the  tem- 
perature will  permit,  as  is  evidenced  by  its  depositing 
this  moisture  upon  the  slightest  fall  in  temperature, 
or  what  is  commonly  termed  by  the  miners  as  the 
''sweating"  of  the  pit.  Air  saturated  with  moisture 
at  a  temperature  of  63°  Fahr.,  which  may  be  taken  as 
the  average  temperature  of  the  pit,  will  weigh  one  per 
cent  lighter  than  dry  air  at  the  same  temperature. 
In  gaseous  mines  the  presence  of  the  pit  gases  will 
change  the  volume  and  the  density  of  the  air-current. 


28  MINE-VENTILATION. 


CHAPTER  IV. 

WORK. 

Prefatory. — Before  entering  further  upon  the  subjec- 
of  "  The  Ventilation  of  Mines,"  let  us  complete  the  pre- 
liminary study  of  forces  by  refreshing  our  memories  in 
respect  to  what  is  termed  in  mechanics  "  Work." 

Definition  of  Work. — A  force  may  exist  in  all  its 
vigor  and  with  unchanging  constancy ;  and  yet  if  that 
force  does  not  move,  or,  in  other  words,  if  it  is  not  ex- 
erted through  a  certain  distance,  it  accomplishes  no 
work.  By  work  we  understand  a  force  exerted  through 
a  certain  distance.  The  force  and  the  distance  through 
which  it  acts  together  become  the  measure  of  the  work 
performed.  In  other  words,  a  force  multiplied  by  the 
path  over  which  it  has  travelled  represents  the  work  of 
that  force. 

Unit  of  Work. — The  adopted  unit  of  work  is  the 
work  performed  by  a  pound  avoirdupois  falling  through 
n  vertical  height  of  a  foot,  or  that  of  a  pound  pres- 
sure moving  through  a  distance  of  a  foot.  This  unit  is 
called  in  mechanics  a  "Foot-pound." 

Power. — When  we  speak  of  power,  we  mean  the  abil- 
ity to  accomplish  a  certain  work  in  a  certain  time.  A 
boy  may  perform  the  work  of  a  man  if  he  is  given  time 
enough,  or  a  man  may  do  the  work  of  ten  men  in  a 
longer  period  of  time. 

Unit  of  Power. — The  unit  of  power  is  a  unit  of  work 
performed  in  a  unit  of  time.  The  adopted  unit  of  power 


WORK.  29 

• 

is  the  work  performed  -by  a  pressure  of  a  pound  acting 
through  a  distance  of  a  foot  in  precisely  one  minute  of 
time.  A  unit  of  power  will  raise  one  pound  avoirdu- 
pois through  a  vertical  height  of  one  foot  in  one  min- 
ute of  time. 

Horse-power.  —  A  horse-power  is  the  power  that  will 
raise  33,000  pounds  through  a  vertical  height  of  one 
foot  in  one  minute  of  time. 

Work  as  a  Measure  of  Power.  —  Work,  then,  is  the 
measure  of  a  power.  The  same  power  will  always  per- 
form the  same  amount  of  work  in  the  same  time, 
though  the  work  may  differ  in  its  kind.  If  we  apply 
the  same  power  to  mines  offering  different  resistances, 
the  work  performed  in  each  case  will  be  the  same,  be- 
cause the  power  is  the  same  ;  the  velocities  and  the 
pressures  may  vary,  according  as  the  relative  areas  and 
lengths  of  the  airways  vary  ;  but  even  under  these 
changing  conditions  the  same  power  will  always  accom- 
plish the  same  amount  of  work. 

Expression  for  Work.—  Assume  the  following  : 

U  =  work  performed  by  a  ventilating  current  ; 

p  =  unit  of  pressure  of  the  established  current  ; 

v  =  veloc.  in  ft.  per  min.  of  the  established  current  ; 

a  =  sectional  area  of  the  airways. 
Then  from  the  definition  of  work  we  may  write 


(X) 

Substituting  for  p  in  equation  (X)   its  value  taken 
from  equation  (VIII),  and  reducing,  we  have 


(XI) 

Again,  we  know  that  the  sectional  area  of  an  airway, 
multiplied  by  the  velocity  of  the  passing  air  (in  feet  per 


30  MINE-VENTILATION. 

minute),  will  give  the  quantity  Q  of  air  passing  per 
minute,  expressed  in  cubic  feet,  which  gives  the  expres- 
sion 

Q-av  .......     (i) 

Substituting  in  equation  (X)  for  av  its  value  Q,  we 
have 

U=QP  ...... 


Again,  referring  to  expression  (i-XII),  and  solving  with 
respect  to  v,  we  have 


Squaring  both  members  of  this  equation  and  substitut- 
ing the  value  of  v1  thus  found  in  equation  (VIII),  we 
have 


Finally,  substituting  this  value  of  p  in  equation  (XII), 
we  have 

U=k±ff.    .     .    .     (XIII) 


RESULTANT   FACTORS   OF   VENTILATION.  31 

CHAPTER    V. 

RESULTANT  FACTORS  OF  VENTILATION. 
VELOCITY,    QUANTITY,    ETC. 

Resume. — We  have  thus  far  considered — 

1st.  The  natural  conditions  obtaining  in'a  pit; 

2d.  Force  as  applied  to  the  air-current ; 

3d.  The  resistance  of  the  mine  opposed  to  such  force  ; 

4th.  Work  as  a  measure  of  power. 

While  we  have  developed  some  important  formulas 
incidentally,  yet  our  study  has  been  thus  far  largely 
preliminary. 

Prefatory. — We  will  now  consider,  separately  and  in 
order,  the  various  factors  of  ventilation  that  result  from 
the  application  of  force  to  overcome  resistance,  or  of 
power  to  produce  work. 

Velocity. — We  have  seen  that  movement  results 
from  the  application  of  pressure  to  air  when  such  pres- 
sure is  not  wholly  resisted.  Such  movement  of  the  air 
in  and  through  the  airways  is  the  velocity  referred  to. 
It  is  uniform,  and  proportionate  to  the  cube  root  of  the 
power  and  also  to  the  square  root  of  the  ventilating 
pressure  (under  like  conditions  of  rubbing  surface  in 
the  airways).  This  is  readily  seen  from  equations  (XVI) 
and  (XVII),  below. 

Expressions  for  Velocity. — We  have  already  seen, 
from  equation  (i-XIII)  that 

»  =  (XIV) 


32  MINE-VENTILATION. 

From  equation  (X)  we  have 


Again,  solving  equation  (XI)  with   respect   to   v,  we 
have 


(XVI) 


And,  further  solving  equation  (VIII)  with  respect  to  the 
same  quantity,  we  have 


Quantity.  —  The  term  "  Quantity,"  as  used  in  refer. 
ence  to  mine-ventilation,  means  the  number  of  cubic 
feet  of  air  passing  any  given  point  in  the  airway  per 
minute. 

Expressions  for  Quantity.  —  We  have  seen  before 
(eq.  (i-XII))  that 

Q  =  av  .......     (XVIII) 

Solving  equation  (XII)  with  respect  to  Q,  we  have 

Q  =  j  ........  (XIX) 

Solving  equation  (2-XIII)  with  respect  to  Q,  we  have 


RESULTANT  FACTORS   OF   VENTILATION..  33 

Again,  substituting  in  equation  (XIX)  for  U  its  value 
taken  from  equation  (XI),  we  have 

Q  =  —  ......     (XXI) 

Finally,  solving  equation  (XIII)  with  respect  to  Q,  we 
have 


Pressure.  —  We  have  seen  before  (eq.  (2-XIII)),  that 

p-k-ff  .....    (XXIII) 
a 

Equation  (VIII)  represents  another  expression  for  pres- 
sure ;  it  is  repeated  here  to  place  these  different  expres- 
sions together  : 

p=  ~  ......     (VIII) 

Combining  equations  (XII)  and  (XXII),  and  solving 
with  respect  to  /,  we  have 


(XXIV) 


Work.  —  (For  the  expressions  of  work,  see  Chapter 
IV.) 

Potential  Factor.  —  The  term  Potential  Factor,  as 
used  in  this  work,  is  a  term  of  special  significance.  It 
always  has  a  value  peculiar  to  the  mine  in  question,  and 
which  represents  for  that  particular  mine  the  relation 


34  MINE-VENTILATION. 

which  will  subsist  between  the  quantity  of  air  passing 
and  the  cube  root  of  the  power  necessary  to  pass  such 
quantity.  Referring  again  to  equation  (XXII),  and  di- 
viding both  members  of  the  equation  by  the  cube  root 
of  U,  we  have 

-T~  =   —.  (XXV) 

Yu        ' 


The  first  member  of  equation  (XXV)  expresses  the 
value  of  the  potential  in  terms  of  the  quantity  and  the 
power  :  this  expression  we  call  the  potential  factor  of 
ventilation.  The  second  member  of  the  equation  ex- 
presses the  value  of  the  same  potential  in  terms  of  the 
minf?  :  we  call  it  the  potential  factor  of  the  mine. 
Expression  for  the  Potential  Factor.  —  Assume 

X  =  potential,  referred  to  ventilation  or  to  the  mine. 

Then  from  the  definition  of  the  potential  factor  we 
write 

....  (xxvi) 


and  also 

*  =  -£=.     •     •     •      (XXVII) 

Vks 

Expressions  in  Terms  of  the  Potential. — Substi- 
tuting successively  in  equations  (XIII),  (XX),  (XXII), 
(XXIII),  and  (XXIV)  the  symbol  X  for  its  value,  as 
given  by  equation  (XXVII),  we  obtain  the  following; 

tf  =C;  (xxviii) 


RESULTANT  FACTORS  OF  VENTILATION.     35 

Q  =  X%U\     ....     (XXX) 
/  =  tL ; (XXXI) 

#==    VJT. (XXXII) 

Quantity  Due  to  Two  Motors. — Assume  the  fol- 
lowing: 
q  =  the  quantity  due  to  an%y  motor  (as  a  fan  running  at 

a  fixed  speed)  working  alone ; 
£t  =  the  quantity  due  to  any  other  motive  source  (as 

another  fan  or  a  furnace)  working  alone ; 
Q  =  the  quantity  due  to  the  simultaneous  action   of 

both  motors. 

Let  u,  «lf  and  U  represent  the  work  performed  in 
passing  the  quantities  <?,  q^  and  Q,  respectively.  Then, 
referring  to  equation  (XIII),  we  write,  for  the  work 
performed  in  each  of  the  three  cases  respectively, 

«=£?"; •  (0 

«,  =  **/;  (2) 

a '.l  ^  } 


(3) 


Now,  when  both  of  these  motors  are  working  simulta- 
neously, or  when  any  number  of  motors  are  working 
and  throwing  air  into  the  same  airways,  each  will  per- 
form its  respective  work,  the  same  as  when  working 


36  MINE-VENTILATION. 

singly  ;  for  the  work  in  each  case  depends  solely  upon 
the  power  applied,  which  we  assume  remains  un- 
changed. Hence  we  write 

U=«  +  *t  ......      (4) 


Now  by  substituting  in  this  last  equation  the  several 
values  of  u,  u^  and  U,  as  given  by  equations  (i),  (2), 
and  (3),  above,  and  dividing  throughout  by  the  common 

factor  (—5),  we  have 

<2'  =  23  +  ^l   .....    (5) 

and  extracting  the  cube  root  of  each  member  of  the 
above  equation  we  find,  for  the  value  of  Q, 


Q  =      f  +  q*m      ...  (XXXIII) 

Expression  for  Head-of-air  Column  in  Terms 
of  Temperature  and  Motive  Height.  —  Referring  to 
equation  (III),  we  find  an  expression  for  ventilating  pres- 
sure P,  in  terms  of  the  temperatures  of  two  air-col- 
umns, which  may  be  the  upcast  and  downcast  shafts, 
respectively.  Let  us  assume 

/  =  average  temperature  of  the  downcast  shaft  ; 

/!  =  average  temperature  of  the  upcast  shaft. 

Then,  dividing  both  members  of  equation  (III),  by  a 
and  substituting  the  value  of  p  thus  found  in  equation 
(II),  and  reducing,  we  have 


H  = 


(**  ~  *  \  (XXXIV) 

H59  +  V 


Expression  for  Horse-power.  —  As  we  have  already 
seen,  a  single  horse-power  is  equivalent  to  33,000  foot- 


RESULTANT   FACTORS   OF  VE 


pounds,  or  units  of  work  ;  hence,  indicating  horse-power 
by  the  symbol  H.  P.,  we  have 

(XXXV) 
33000 

Pressure  in  Terms  of  Water-gauge. — The  unit  of 
ventilating  pressure,  as  indicated  by  inches  of  water- 
gauge,  is  calculated  from  the  weight  of  a  cubic  foot  of 
water.  One  cubic  foot  of  water  at  a  temperature  of 
62°  F.  weighs  62.355  pounds;  and  one  inch  of  water- 
gauge  will  represent  a  pressure  per  square  foot  of  y1^  of 
this,  or,  say,  5.2  pounds.  Assume 

i  =  inches  of  water-gauge. 

Then  we  may  write 

/=5.2£     ....     (XXXVI) 

Pressure  in  Terms  of  Temperature  and  Motive 

Height.— Combining  equations  (II)  and  (XXXIV),  and 
solving  with  respect  to  /,  we  have 


p  =  A  x      .-      .  (XXXVII) 

r  459  +  *        459+'.   V  ' 


38  MINE-VENTILATION. 


CHAPTER  VI. 

EXPRESSION  FOR  STRAIGHT-PADDLE  FANS. 

Prefatory. — In  Chapter  II  we  developed  an  expres- 
sion for  the  static  pressure  due  to  the  action  of  a  fan  ; 
we  are  now  prepared  to  formulate  an  expression  for  the 
work  a  straight-paddle  fan  is  capable  of  performing,  in 
terms  of  itself.  Afterward,  by  equating  this  work  and 
the  work  necessary  to  be  performed  in  a  mine  in  order 
to  pass  a  certain  quantity  of  air  (Q)  per  minute  (eq. 
XIII),  we  obtain  an  expression  for  the  quantity  of  air 
a  fan  will  yield  per  minute  in  terms  of  itself  and  the 
mine  at  which  it  is  working.  This  is  one  of  the  most 
important  determinations  in  the  subject  of  mine-ven- 
tilation ;  the  general  method  of  procedure  has  been 
outlined  in  the  introductory  chapter,  to  which  refer- 
ence should  now  be  made. 


FIG.  III. 


Weight  of  Air  in  One  Section  of  the  Fan, — Let 
Fig.  (Ill)  represents  one  section  of  a  straight-paddle  fan, 


EXPRESSION   FOR   STRAIGHT-PADDLE   FANS.         39 

showing  the  space  between  two  consecutive  blades. 
Assume  as  under  equation  (V).  Combining  equations 
(5~V),  and  (6-V),  we  have,  for  the  weight  of  air  in  one 
section  of  the  fan, 

K/=  «(&  -*•')*  x  I>3253  XB          (n 

«t  459  +  * 

Centrifugal  Force  of  this  Weight.  —  We  have  for 
the  centrifugal  force  developed  in  one  section  of  the 
fan,  as  given  by  equation  (2-V), 


Measure  of  this  Centrifugal  Force.  —  A  force  is 
measured  by  the  velocity  it  can  create  in  a  unit  of  mass 
in  one  second  of  time;  this  measure  /is  called  the  ac- 
celeration due  to  the  force  F,  and  means  feet  per  sec- 
ond. But  our  centrifugal  force  .Facts  upon  a  number 
of  units  of  mass  m  ;  hence  its  measure  is  expressed 
by  the  equation 

F  =  fm  ........     (3) 

In  this  equation  (3)  m  is  the  mass  of  the  weight  W  '; 

IW\ 

hence  we  may  substitute  for  it  its  value  (  —  J,  and  we 

have 


Combining  equations  (2)  and  (4),  above,  and  solving  with 
respect  to  /,  we  have 


40  MINE-VENTILATION. 

Then,  squaring  both  members  of  equation  (3~V),  and 
substituting  the  value  of  v?  thus  found  in  equation  (5), 
above,  and  reducing,  we  have 

f  =--  0.010966  R,  n*  .....     (6) 

Work  of  the  Centrifugal   Force  per  Second.— 

Equation  (6),  above,  gives  the  value  of/",  the  accelera- 
tion due  to  the  force  Ft  which  we  must  remember  acts 
radially.  But  when  the  force  is  uniformly  accelerative, 
that  is  to  say,  when  the  force  is  constant  and  acts  to 
increase  the  velocity  of  the  mass  by  a  constant  quantity 
each  unit  of  time,  the  space  passed  over  during  such 
unit  of  time  will  be  equal  to  one  half  of  the  acceleration 

(—  )  ;  and,  as  we  have  seen  from  Chapter  IV,  the  work 

of  this  force  F  during  one  second  of  time  is  equal  to 
the  force  multiplied  by  this  space  over  which  it  has 
passed  in  one  second  of  time.  Assume  the  following: 
u  —  the  work  performed  in  one  second  by  one  section 

of  the  fan  only  ; 
£/,  =  the  total  work  performed   in  one  second  by  all 

the  sections  of  the  fan  ; 
[7=  the  total  effective  work  performed  by  the  fan  in 

one  minute  of  time. 
Then  we  have,  from  what  has  preceded, 


Work  of  the   Fan  per   Second.  —  For   the  entire 
work  of  the  fan  per  second 


(8) 


EXPRESSION   FOR   STRAIGHT-  PADDLE   FANS.        4! 

Combining  equations  (4),  (6),  and  (8),  above,  and  reduc- 
ing, we  have 

W 
Ul  =  ^  —  0.000060  1  2R*n4  .....     (9) 

o 

Now,  substituting  for  W  and  R^  their  respective  values, 
as  taken  from  equations  (i),  above,  and  (4~V),  and 
reducing,  equation  (9),  above,  becomes 

U,  =  0.000005  1  MbRJJ?  -  R*)  —  ^—  .     (10) 

Effective  Work  of  the  Fan  per  Minute.  —  Equa- 
tion (10),  above,  gives  the  expended  work  of  the  fan  for 
one  second  of  time.  Multiplying  this  work  for  one 
second  by  60,  to  obtain  the  work  for  one  minute,  and 
introducing  a  coefficient  K  of  efficiency  (to  be  ex- 
plained in  Chapter  VIII.  —  "  Economic  Discussion  of 
the  Fan"),  we  obtain  for  the  effective  work  of  the  fan, 
for  a  minute  of  time,  the  following  equation  : 


U=  Q.ooo3iiiKn4l>R,(R'-R^—~.  (XXXVIII) 

Quantity  yielded  per  Minute  in  Terms  of  the  Fan 
and  Mine.  —  Equation  (XXXVIII)  gives  the  entire 
effective  work  of  the  fan  for  one  minute  of  time.  This 
effective  work  of  the  fan  must  of  necessity  be  equal  to 
the  work  U  performed  in  one  minute  by  the  ven- 
tilating current  in  the  pit,  and  which  is  expressed  by 
equation  (XIII).  Therefore,  equating  these  values  of 
U  and  solving  with  respect  to  <2,  we  have 


=  0.06776  1/^1  Kn*bR,(R*-R?')       B     (XXXIX) 
ks  459+^- 


42  MINE-VENTILATION. 

Equation  (XXXIX)  is  the  general  equation  for  deter- 
mining the  yield  of  a  straight-paddle  fan,  running  at  a 
fixed  speed,  at  any  given  mine,  the  temperature  and 
barometric  pressure  being  also  given.  But  care  must 
be  taken  in  its  application  that  the  effect  of  other 
agencies  of  ventilation  are  taken  into  account,  such  as 
upcast  shafts  heated  by  the  natural  heat  of  the  mine, 
and  dips  or  rises  in  the  entries :  these,  as  well  as  small 
break-throughs,  obstructed  airways,  etc.,  etc.,  are  sour- 
ces very  often  productive  of  error. 

Pressure  yielded  by  a  Fan.— We  often  hear  the 
question  asked,  "  What  pressure  or  water-gauge  will 
the  fan  give?"  If  the  fan  in  question  is  working  into 
a  closed  space,  thereby  creating  a  certain  static  pres- 
sure, the  question  is  a  proper  one.  But  when  the  fan 
is  throwing  air  into  a  certain  mine,  the  pressure  referred 
to  is  created  by  the  resistance  of  the  mine  :  it  depends 
directly  upon  this  resistance.  The  same  fan,  running 
at  the  same  speed,  but  throwing  air  into  another  mine, 
will  establish  a  different  pressure,  according  to  the  re- 
sistance to  be  overcome.  In  any  case  of  mine-ventila- 
tion, whether  the  motor  is  a  fan  or  otherwise,  the  ven- 
tilating pressure  may  be  found  by  applying  equation 
(XXIII). 

Horse-power  of  a  Fan. — By  combining  equations 
(XXXV)  and  (XXXVIII),  and  solving  with  respect  to 
H.P.,  we  have 

H.P.  =  o.oooocxx)0943^4^^3-^13)— A- 

459+*- 


ECONOMIC   DISCUSSION   OF  THE   FURNACE.        43 


CHAPTER  VII. 

ECONOMIC  DISCUSSION  OF  THE  FURNACE. 

Prefatory.— It  does  not  belong  to  the  province  of 
this  work  to  discuss  the  comparative  merits  of  differ- 
ent ventilating-machines ;  nor  to  remark  upon  their 
construction,  only  as  such  construction  may  interfere 
with  the  theoretical  efficiency  of  the  machine.  Such 
economic  construction  relative  to  the  furnace  must 
provide — 

First,  a  sufficient  grate-area  for  the  burning  of  the 
required  amount  of  coal  to  produce  the  ventilating 
pressure  Pin  that  particular  mine; 

Second,  a  sufficient  flue-area  or  airway  over  and 
around  the  fire,  so  as  not  to  obstruct  the  flow  of  the 
quantity  Q. 

There  are  other  essential  points  in  furnace  construc- 
tion, but  these  are  the  only  ones  that  affect  the  effi- 
ciency of  the  furnace. 

Economic  Grate-area. — By  the  economic  grate-area 
is  meant  such  an  area  of  the  grate  of  a  furnace  as  will 
burn  a  given  amount  of  coal  in  a  given  time  and  there- 
by give  to  the  furnace  a  certain  heating  capacity,  or, 
in  other  words,  render  the  furnace  capable  of  creating 
a  temperature  tb  in  a  current  Q  of  mixed  air  and  gases 
passing  over  and  around  it, 

How  Determined. — In  order  to  determine  the  area 
of  grate  needed  to  cause  a  given  rise  of  temperature 


44  MINE-VENTILATION. 

in  a  given  current  of  mixed  air  and  gases,  we  must  as- 
certain the  following. 

First,  the  constituents,  by  weight,  of  the  gaseous 
current  and  their  respective  specific  heats,  from  which 
the  power  of  the  current  to  absorb  heat  is  calculated  ; 

Second,  the  heating  power  of  a  pound  of  coal,  or,  as 
we  say,  the  number  of  thermal  units  contained  therein  • 

Third,  the  square  feet  of  grate-area  required  for  the 
combustion  of  a  given  weight  of  coal  per  hour  ; 

Fourth,  the  required  rise  in  the  temperature  of  the 
upcast  current. 

These  data  form  the  basis  of  the  calculation.  It  is 
a  practical  problem  in  ventilation,  and  is  by  no  means 
technical  or  theoretical.  It  requires  no  actual  analysis 
of  the  gaseous  current  to  determine  its  exact  character 
for  our  purposes.  What  we  must  base  our  calculations 
upon  is  the  worst  possible  state  of  the  current  with 
respect  to  gases  and  moisture,  so  that  the  results  will 
be  sufficiently  large  to  meet  any  demand.  Fortunately 
this  extreme  condition  is  determinable  both  with  re- 
spect to  gases  and  moisture.  Having  determined  the 
several  constituent  gases  and  vapors,  we  multiply  the 
weight  of  each  of  these  by  its  respective  specific  heat, 
and  take  the  sum  of  these  products  ;  multiply  this  sum 
by  the  required  rise  of  temperature  ;  finally,  divide  this 
last  product  by  the  thermal  units  contained  in  a  pound 
of  coal :  the  quotient  thus  obtained  will  be  the  weight 
of  coal  to  be  burned.  The  grate-area  is  then  propor- 
tioned to  this  weight  of  coal,  according  to  our  experi 
ence  and  established  rules. 

Condition  of  Upcast  Current. — As  the  calculations 
and  reasonings  incident  to  such  an  investigation  are  to 
some  extent  complicated,  though  by  no  means  diffi- 


ECONOMIC   DISCUSSION   OF   THE   FURNACE.        45 

cult,  and  as  the  general  reader  may  not  care  to  devote 
the  time  or  patience  necessary  to  a  clear  understanding 
of  the  details,  we  have  tabulated  in  concise  form  the 
various  factors  entering  the  discussion,  showing  their 
final  combination  to  produce  the  equation  referred  to 
above.  This  equation  will  be  deduced  in  detail  in  the 
latter  part  of  this  chapter.  The  table  referred  to  is 
Table  II  of  the  Appendix. 

Dry  Shafts. — We  will  now  consider  the  practical 
application  of  equation  (XLIV),  which  applies  to  dry 
shafts,  and  afterward  explain  its  development  in  detail, 
taking  up  also,  in  the  same  connection,  the  data  refer 
ring  to  wet  shafts.  In  this  equation  0  represents  the 
tension  of  aqueous  vapor  at  the  temperature  /4,  its 
value  being  taken  from  Table  III  of  the  Appendix ; 
t^  is  the  temperature  of  the  return  current  just  pre- 
vious to  its  entering  the  influence  of  the  furnace ;  its 
value  may  be  assumed  to  be  as  low  as  70°  F. :  if  in  any 
instance  it  has  a  higher  value  than  this,  the  furnace  is 
thereby  aided  in  its  work ;  but  we  must  assume  such 
probable  values  as  to  make  our  calculation  safe,  and 
cover  the  case  that  will  make  the  greatest  demand  upon 
the  furnace.  The  value  of  /5,  the  temperature  of  the 
lower  end  of  the  upcast,  will  depend  upon  the  quantity 
of  air  to  be  furnished  and  the  depth  of  the  shaft. 

Illustration. — To  illustrate :  Let  us  suppose  we  are 
about  to  open  a  mine,  to  be  ventilated  by  a  furnace, 
and  we  wish  to  provide  for  a  capacity  of,  say,  500  tons 
of  coal  per  day.  We  must  figure  upon,  say,  240  men, 
including  trappers  and  company  men,  and,  say,  6  mules. 
If  we  give  each  man  100  cu.  ft.  of  air  per  minute,  and  each 
mule  500  cu.  ft.  per  minute,  we  shall  require  27,000  cu.  ft. 
per  min.  travelling;  but,  as  we  must  provide  against 


46  MINE-VENTILATION. 

every  exigency, — gob-fires,  poor  stopings,  obstructed 
air-courses,  etc.,  etc., — it  will  not  be  safe  to  estimate 
upon  less  than  30,000  cu.  ft.  of  air  per  minute  in  circula- 
tion. In  this  problem  the  values  assumed  are  taken 
as  existing,  adopted,  or  possible  limiting  values  of  the 
various  factors  of  ventilation.  We  will  suppose  that 
the  inlet  and  discharge  openings  are  shafts  of  the  same 
depth,  and  the  seam  of  coal  maintains  a  practical  level 
throughout  the  pit. 
Assume  the  following : 

h  =  900  ft motive  height. 

a  =  50  sq.  ft sec.  area  of  airway. 

s  =  120,000  sq.  ft rubbing  surf,  of  airway. 

Q  =  30,000  cu.  ft at  temp.  tv 

£,  =  32°  F avg.  temp,  of  downcast. 

/3  =  60°  F.temp.  of  air  where  quant,  is  taken. 
t^  =  70°  F.temp.  of  air  before  reaching  furn. 
/B  =  (?)...  .temp,  of  air  at  bottom  of  upcast. 

tfj  =  (?) avg.  temp,  of  upcast. 

B  =  30" height  of  barom. 

^  =  28,800  sq.  ft cooling  surf,  of  shaft. 

(Size  of  air-shaft,  8'  X  8'.) 

£,  =  0.5 (relative)  coef.  of  cooling. 

C  =  (?) pounds  of  coal  burned  per  h. 

G  =  i/io  C grate-area  of  furn. 

First  determination  :  The  first  step  in  our  problem 
is  to  determine  the  unit  of  ventilating  pressure  that  will 
circulate  the  given  quantity  of  air  (30,000  cu.  ft.)  per 

minute,  against  the  potential VT7P/  363.432.  Referring 
to  (equation  XXXI),  and  substituting  therein  the  above 


ECONOMIC   DISCUSSION   OF  THE   FURNACE.        47 

numerical  values,  which  we  have  assumed,  and  reduc- 
ing, we  have 

/  =  18.748  Ibs. 

Second  determination:  The  next  step  is  to  determine 
the  average  temperature  tl  of  the  upcast  shaft  which 
will  produce  the  above  unit  of  pressure.  By  substitut- 
ing in  equation  (XXXVII)  the  above  assumed  values 
and  the  value  of/  just  found,  and  solving  with  respect 
to  /t,  remembering  that  /2,  the  temperature  of  the 
downcast  shaft,  is  the  same  as  /,  the  temperature  of  the 
outside  air,  in  this  case,  we  find,  after  reducing, 

/,  =  202°  Fahr. 

Third  determination  :  The  next  step  is  to  determine 
the  necessary  temperature  of  the  bottom  of  the  upcast 
shaft  in  order  to  produce  the  average  temperature 
just  determined  above.  By  substituting  in  equation 
(XLVI),  hereinafter  deduced,  the  numerical  values 
thus  far  assumed  and  determined,  and  reducing,  we 
find 

*§  =  327°  Fahr. 

Fourth  determination  :  The  final  step  in  our  problem 
is  to  determine  the  weight  of  coal  that  we  must  burn 
per  hour  upon  the  grate  in  order  to  produce  the  re- 
quired rise  in  the  temperature  of  the  air-current.  We 
have  assumed  the  temperature  /4  of  the  air  just  pre- 
vious to  its  entering  the  influence  of  the  furnace  to 
be  70°  Fahr.,  while  the  required  temperature  after 


48  MINE-VENTILATION. 

passing  the  furnace  we  found  must  be  327°.  This 
requires  a  rise  in  temperature  due  to  the  heat  of 
the  furnace  of  257°.  Now,  referring  to  equation 
(XLIV)  hereinafter  deduced,  and  substituting  therein 
the  above  numerical  values,  assumed  and  determined 
(taking  the  value  of  0,  for  a  temperature  of  70°  F., 
from  Table  III  of  the  Appendix),  and  reducing,  we  find 

C  =  648  Ibs. 

Knowing  the  weight  of  coal  to  be  burned  per  hour 
in  pounds,  it  is  usual  to  assume  one  tenth  of  this  weight 
as  the  area  in  square  feet  of  the  grate  best  adapted 
for  the  economic  combustion  of  such  amount  of  coal. 
Hence  in  this  case  we  find 

G  =  65  sq.  ft. 

Wet  Shafts.— When  the  shaft  is  wet  there  will  be 
an  additional  amount  of  coal  necessary,  beyond  the 
amount  required  for  heating  the  current,  to  evaporate 
the  moisture  of  the  shaft  and  raise  the  temperature  of 
the  vapor  thus  formed  to  the  temperature  of  the  cur- 
rent. Continuing  the  above  illustration,  which  refers 
only  to  a  dry  shaft,  let  us  now  assume  the  same  shaft 
to  be  making,  say,  four  barrels  of  water  per  hour,  or 
about  1000  pounds.  Assuming  the  average  tempera- 
ture of  evaporation  /„  to  be  126°  F.,  and  making  the 
necessary  substitutions  in  equation  (XLV)  and  reducing, 
we  find,  for  the  additional  amount  of  coal  necessary  on 
account  of  the  wet  condition  of  the  shaft, 

C  =  80  Ibs.  (extra). 


ECONOMIC   DISCUSSION   OF  THE  FURNACE.        49 

Adding  this  to  the  amount  of  coal  determined  pre- 
viously in  the  case  of  the  dry  shaft,  we  obtain  for  the 
total  amount  of  coal  required  to  be  burned  per  hour,  in 
this  case,  728  pounds,  which  gives  for  the  grate-area 
required 

G  =  73  sq.  ft. 

Suggestions. — The  furnace  should  always  be  built 
with  airways  or  coolers  above  and  on  each  side.  The 
sectional  area  of  such  airways  should  not  be  less  than 
the  sectional  area  of  the  entries. 

Relative  Quantities. — The  quantity  of  air  Q&  will  be 
larger  than  the  original  quantity  Q,  owing  to  a  rise  of 
temperature  from /3  to/5;  the  relation  between  these 
volumes  or  quantities  being  expressed  by  the  propor- 
tion 

G:  0B  ::  459  +  ',  :  459  +  '.; 
whence  we  have 

^"  •  •  •  (XLI> 

in  which  Q  and  <2B  are  the  quantities  or  volumes  of 
air  at  the  temperatures /3  and  /^respectively.  From 
this  equation  we  see  that  the  volume  of  the  current 
may  be  increased  from  30$  to  50$  by  the  heat  of  the 
furnace. 

Suggestions. — The  increase  of  quantity  referred  to 
above  is  usually  compensated  for  by  a  corresponding 
increase  in  velocity  passing  the  furnace.  Hence,  if  the 
pit  is  free  from  large  gas  feeders,  it  will  be  sufficient  to 
provide  a  sectional  area  passing  the  furnace  equal  to 
the  area  of  the  entries.  Coal  for  supplying  the  furnace 


50  MINE-VENTILATION. 

should  be  stored  in  cuts,  in  the  rib  made  for  the  pur- 
pose, and  not,  as  is  often  done,  deposited  in  the  air- 
way, in  front  of  the  furnace,  or,  worse  still,  left  in  the 
car,  standing  in  the  air-course  till  needed.  The  loaded 
car  should  be  switched  into  the  cut  in  the  rib  and  the 
coal  used  from  it  as  needed,  to  save  handling  the  coal 
twice. 

We  have  thus  far  illustrated  the  practical  application 
of  the  formulas ;  the  remainder  of  the  chapter  will  be 
devoted  to  explaining  their  development  in  detail,  for 
the  benefit  of  the  student,  and  may  be  passed  over,  if  so 
desired,  by  the  general  reader. 

Thermal  Unit. — The  unit  upon  which  all  calcula- 
tions are  based,  in  investigations  relative  to  the  heat- 
ing power  of  coal,  is  called  the  "Thermal"  unit.  It  is 
the  amount  of  heat  absorbed  in  raising  one  pound  of 
water  one  degree  in  temperature. 

French  Unit — American  Unit. — The  French  use  a 
unit  referred  to  the  Centigrade  scale,  and  this  unit  con- 
tains more  heat  than  our  American  unit,  which  is  re- 
ferred to  the  Fahrenheit  scale..  The  ratio  between 
these  two  units  is  expressed  by  the  fraction  -§-. 

Calorics  of  Coals. — Different  coals  possess  different 
calorific  powers,  and  hence  contain  a  greater  or  less 
number  of  thermal  units  to  the  pound.  Experience 
has  placed  the  calorific  value  of  bituminous  coal,  how- 
ever, at  8000  thermal  units  to  the  pound  of  coal  in  the 
French  system,  or  14,400  units  in  the  American  sys- 
tem. In  common  practice  bituminous  coal  is  assumed 
to  contain  14,000  American  thermal  units.  These  units 
are  often  spoken  of  as  the  calorics  of  the  coal :  they  rep- 
resent the  amount  of  heat  that  coal  is  capable  of  giving 
out  when  burned. 


ECONOMIC   DISCUSSION   OF  THE   FURNACE.         5 1 

Calorific  Capacity. — Different  solids,  such  as  iron, 
copper,  tin,  etc.,  each  absorb  a  different  quantity  of  heat 
for  a  rise  of  one  degree  in  their  temperature.  Different 
liquids,  such  as  water,  oil,  etc.,  absorb  likewise  differ- 
ent quantities  of  heat  for  the  same  rise  of  temperature. 
So  also  different  gases,  including  air,  each  absorb  dif- 
ferent quantities  of  heat  for  a  rise  of  one  degree  in 
their  temperature. 

Specific  Heat — The  amount  of  heat  thus  absorbed 
by  one  pound  of  any  solid,  liquid,  or  gas,  during  a  rise 
of  one  degree  of  its  temperature,  as  compared  with  the 
amount  of  heat  absorbed  by  one  pound  of  water  dur- 
ing a  like  rise  in  temperature,  is  called  the  "  Specific 
Heat"  of  that  solid,  liquid,  or  gas.  As  the  specific 
gravity  of  any  substance  is  the  ratio  between  the  weight 
of  such  a  substance  and  the  weight  of  a  like  volume  of 
water  at  a  standard  temperature,  so  also  the  specific 
heatoi  any  substance — solid,  liquid,  or  gas — is  the  ratio 
between  the  quantity  of  heat  such  substance  absorbs 
during  a  certain  rise  in  its  temperature,  and  the  quan- 
tity of  heat  absorbed  by  an  equal  weight  of  water 
during  an  equal  rise  in  temperature. 

Specific  Heat  expresses  Thermal  Units. — Now 
the  amount  of  heat  absorbed  by  one  pound  of  water  dur- 
ing a  rise  in  its  temperature  of  one  degree  Fahrenheit 
is  adopted  as  our  thermal  unit.  Hence  it  follows  that 
the  specific  heat  of  any  substance,  solid,  liquid,  or  gas, 
referred  to  water  as  unity,  will  express  at  the  same 
time  the  number  of  thermal  units  required  to  raise  one 
pound  of  that  substance  one  degree  Fahrenheit. 

General  Expression  for  Weight  of  Coal. — If,  now, 
we  multiply  the  specific  heat  of  the  substance  (which 
we  have  just  seen  is  equal  to  the  number  of  thermal 


52  MINE-VENTILATION. 

units  required  to  raise  one  pound  of  the  substance  one 
degree)  by  the  weight  W  of  the  substance  and  then 
by  its  rise  in  temperature,  say  /5  —  /4,  we  shall  obtain 
the  thermal  units  absorbed  by  that  substance  during 
such  rise  in  its  temperature  ;  and,  dividing  this  product 
by  the  thermal  units  contained  in  one  pound  of  coal,  we 
obtain  the  weight  of  coal  necessary  to  burn,  in  order  to 
produce  the  above  rise  in  temperature. 
Assume  the  following  : 

C  =  weight  of  coal  burned  per  hour,  in  pounds; 
W=  weight  of  air  passing,  expressed  in  terms  of  Q, 

at  a  temp.  t%  ; 
Wn  =  weight  of  the  nitrogen  in  the  current,  expressed 

in  terms  of  0,  at  a  temp.  /3  ; 
Wc  —  weight  of  the   carbonic-acid  gas  in  the  upcast 

current,  in  terms  of  Q,  at  a  temp.  /3  ; 
Wv  =  weight  of  the  aqueous  vapor  in  the  saturated  up- 

cast current,  in  terms  of  Q,  at  a  temp.  /8  ; 
6  =  symbol  denoting  specific  heat  ; 
0  =  symbol  denoting  tension  of  aqueous  vapor. 
And  we  may  write,  from  what  has  preceded, 


(XLII) 


I4,OOO 


Equation  (XLII)  is  a  generic  equation,  and  in  it  W 
has  a  general  reference  to  the  weight  of  any  substance. 

Gaseous  Composition  of  Upcast  Current.  —  In  re- 
gard to  the  gaseous  composition  of  the  upcast  cur- 
rent, it  may  be  thought  by  many  to  be  so  variable  as 
to  admit  of  no  practical  solution.  This,  however,  is  not 
the  case.  As  previously  stated,  we  must  consider  such 
a  condition  of  the  current  as  will  make  the  greatest  de- 


ECONOMIC   DISCUSSION   OF   THE   FURNACE.         53 

mand  upon  the  furnace.  Such  a  condition  will  suppose 
all  the  oxygen  of  the  air  to  be  converted  into  carbonic- 
acid  gas  (COa),  as  the  result  of  the  slow  and  active  com- 
bustions of  the  pit  ;  this  gas  being  the  heaviest  gas  that 
could  be  formed  by  the  natural  chemical  reactions. 
This  condition  is  readily  determined  and  the  weights 
of  the  resulting  gases  easily  figured. 

Expression  for  Weight  of  Air  in  Terms  of  Q.— 
We  assume  a  certain  quantity  of  air  Q,  passing  along 
the  intake  of  a  mine,  at  a  temperature  /3,  and,  refer- 
ring to  equation  (I)  and  multiplying  by  Q,  we  have 


w- 


Expression  for  Weight  of  Nitrogen.  —  This  last 
equation  gives  the  weight  of  air  per  minute  passing 
along  the  intake.  Now  we  know  from  the  composition 
of  the  atmosphere  that  y7^-  of  this  weight  is  the  weight 
of  the  nitrogen  contained  in  that  air,  and  which  under- 
goes no  change  in  its  passage  through  the  mine  ;  hence 
we  may  write  for  the  weight  of  the  nitrogen  in  the  up- 
cast current,  remembering  that  the  pressure  borne  is 
the  barometric  pressure  less  the  tension  of  the  vapor  at 
the  temperature  of  saturation  0,4, 


Expression  for  Weight  of  Carboni-accid  Gas.  — 

The  oxygen  of  the  air  is  the  active  agent  in  producing 
and  maintaining  combustion,  either  slow  or  active  ;  and 
in  its  passage  through  the  pit  it  is  converted,  in  greater 


54  MINE-VENTILATION. 

or  less  proportion,  into  carbonic-acid  gas  by  its  chemi- 
cal union  with  carbon,  incident  to  gob-fires,  slow  com- 
bustion of  coal,  burning  of  lamps,  breathing  of  men 
and  animals,  and,  lastly,  the  combustion  of  the  coals  of 
the  furnace.  It  is  readily  seen  that  the  formation  of 
carbonic-acid  gas  is  limited  by  the  amount  of  free 
oxygen  in  the  current  and  that  when  this  oxygen  is 
exhausted  combustion  in  any  form  in  the  pit  ceases  ; 
even  the  furnace  fire  is  smothered  and  extinguished, 
which  sometimes  happens  in  badly  managed  pits.  Now 
we  know  from  the  composition  of  the  atmosphere  that 
•^fg-  of  the  weight  of  air  is  the  weight  of  the  free 
oxygen  in  that  air  ;  and,  again,  this  free  oxygen  when 
converted  into  carbonic-acid  gas  forms  T8T  of  the  weight 
of  that  gas.  Hence  we  may  write 


(2) 


Substituting    in   this   last    equation    for    W,  its  value 
taken  from  equation  (XLIII),  and  reducing,  we  have 


Equation  (3),  above,  presupposes  that  all  the  free  oxygen 
of  the  air  is  exhausted  when  the  bottom  of  the  upcast 
is  reached.  This  is  the  worst  condition  that  can  exist, 
and  will  make  the  heaviest  demand  upon  the  furnace, 
relative  to  gases.  If  combustible  gases  are  present  in 
the  return  current,  it  may  be  assumed  that  such  gases 
will  burn  at  the  furnace,  and  that  the  heat  of  such  burn- 
ing will  be  sufficient  to  raise  the  temperature  of  the  in- 
combustible gases  any  probable  number  of  degrees, 


ECONOMIC   DISCUSSION   OF  THE   FURNACE.         55 

independent  of  the  heat  of  the  furnace ;  such  number 
of  degrees  may  then  be  deducted  from  the  rise  in  tem- 
perature expected  from  the  furnace.  In  some  instances, 
in  fiery  mines,  this  combustion  of  gases  (properly 
aerated)  at  the  furnace  forms  an  essential  element  in 
heating  the  air-current ;  but  it  should  not  be  relied 
upon  to  any  large  extent,  as  a  general  rule,  in  calculat- 
ing the  size  of  a  furnace. 

Expression  for  Weight  of  Vapor  of  Saturation. 
— We  assume  the  air-current  to  be  saturated  with  aque- 
ous vapor  from  contact  with  the  moisture  of  the  pit, 
which  is  always  the  case  upon  its  return,  as  is  evidenced 
by  the  sweating  of  the  roof  and  the  sides  of  the  air- 
ways, wherever  this  current  is  chilled  or  its  temperature 
falls  in  the  least.  The  weight  of  this  vapor  of  satura- 
tion is  easily  determined  (its  specific  gravity  as  referred 
to  air,  at  the  same  temperature  and  pressure,  being 
0.6235  ;  see  Table  V  of  the  Appendix)  by  the  equation 


,  0;    •••   (4) 
4i>y  ~T~  ^3 

or,  reducing, 


Summary. — Equations  (i),  (3),  and  (5),  above,  give  the 
greatest  weight  of  these  three  constituents  possible  in 
a  current ;  and  these  are  the  only  constituents  of  a 
mine-current  which  affect  the  size  of  the  furnace. 

Resume. — We  have  now  determined  the  weight  of 
each  of  the  gases  and  vapors  passing  per  minute  and 

composing   the    upcast    current.     Easlvof  ih^se  gases 
r  ^X«i¥SE   LIBRl^Sc 


56  MINE-VENTILATION. 

and  vapors  possesses  a  different  specific  heat,  as  previ- 
ously stated,  and  this  specific  heat  expresses  the  ther- 
mal units  necessary  to  raise  one  pound  of  each  gas  or 
vapor,  respectively,  one  degree. 

Expression  for  Weight  of  Coal  to  Heat  Air-cur- 
rent (Dry  Shaft).—  Referring  now  to  equation  (XLII), 
which  is  the  general  equation  for  the  required  weight 
of  coal,  and  substituting  in  turn  for  Wits  values  as 
taken  from  equations  (i),  (3),  and  (5),  respectively,  and  for 
6  its  value  for  each  respective  gas  or  vapor  as  given 
in  Table  IV  of  the  Appendix,  and  then  adding  these 
three  resulting  equations  together,  multiplying  by  60 
to  reduce  to  hours,  and  denoting  the  total  coal  required 
by  Clt  we  have  finally,  after  reducing, 


,  =  (0.33945  +  o.oS760,)x.    (XLIV) 


Equation  (XLIV)  gives  the  pounds  of  bituminous  coal 
burned  per  hour  in  raising  the  temperature  of  the  up- 
cast current  from  /4  to  /6  in  a  dry  shaft. 


WET   SHAFTS. 

Prefatory.  —  When  we  have  a  wet  shaft  to  deal  with, 
we  assume  that  the  conditions  are  precisely  the  same 
as  in  a  dry  shaft,  except  that  we  must  burn  an  extra 
amount  of  coal  in  order  to  evaporate  the  moisture  of 
the  shaft  and  to  raise  the  temperature  of  the  vapor  thus 
formed  from  the  temperature  of  evaporation  to  the 
temperature  of  that  portion  of  the  shaft  where  the  va- 
por was  formed. 

Condition  of  Shaft.  —  In  a  wet  shaft,  evaporation  is 


ECONOMIC   DISCUSSION   OF  THE   FURNACE.         $? 

taking  place  all  the  way  up  and  down  the  shaft,  below 
the  point  where  the  moisture  first  makes  its  appearance. 
The  moisture  finds  its  way  through  the  curbing  at  or 
somewhat  below  the  flow,  and  starts  to  trickle  down  the 
sides  of  the  shaft :  this  water  may  or  may  not  all  find 
its  way  to  the  bottom  of  the  shaft,  according  to  the 
strength  of  the  flow ;  it  may  all  be  evaporated  before 
the  bottom  is  reached,  as  the  evaporation  is  constantly 
going  on. 

Temperature  of  Evaporation. — The  evaporation 
from  the  sides  of  the  shaft  is  taking  place  at  all  tem- 
peratures, from  the  temperature  of  the  percolating  wa- 
ter, which  we  assume  to  be  40°  F.,  to  the  temperature 
at  which  boiling  takes  place,  212°  F.  Wet  boards  steam- 
ing in  the  cold  air,  or  wet  clothes  drying  in  the  wind, 
are  every-day  examples  of  evaporation  taking  place  at 
low  temperatures. 

Absorption  of  Heat. — Evaporation  at  any  temper- 
ature is  always  accompanied  by  an  absorption  of  heat, 
which  becomes  latent  in  the  vapor.  This  absorption  of 
heat  by  the  vapor  cools  the  upcast  current.  Accord- 
ing to  the  experiments  of  Regnault  upon  the  absorp- 
tion of  heat  by  vapors,  and  which  are  more  conclusive 
than  the  experiments  of  Watt  upon  the  same  subject, 
this  absorption  of  sensible  heat  varies  as  the  tempera- 
ture of  evaporation  varies.  The  absorption  will  there- 
fore be  much  greater  in  the  lower  part  of  the  shaft 
where  the  temperature  often  reaches  the  boiling-point. 
The  effect  of  this  absorption  is  to  assimilate  the  tem- 
peratures of  the  upper  and  lower  parts  of  the  shaft, 
bringing  them  nearer  to  the  average  temperature :  the 
vapor  acts  as  a  carrier  of  the  heat  from  the  lower  to 
the  upper  part  of  the  shaft,  absorbing  it  in  the  lower  and 


58  MINE-VENTILATION. 

condensing  and  giving  it  up  again  in  the  upper  cooler 
portions.  This  heat  of  vaporization  or  latent  heat  is 
expressed  by  the  empirical  formula  of  Regnault  ;  as  is 
also  the  heat  absorbed  in  raising  the  temperature  of 
the  vapor,  after  it  is  formed,  to  the  temperature  of  that 
part  of  the  shaft. 

Expression  for  Extra  Coal  (Wet  Shaft).— These 
formulas  of  Regnault  are  empirical,  but  none  the  less 
valuable,  as  the  experiments  were  carefully  made  and 
the  experimenter  himself  reliable. 

Assume  the  following : 

w  =  wt.  of  water  (approx)  shaft  makes  per  hour,  in 

pounds ; 

/,  =  average  temp,  of  upcast  shaft ; 
/,  =  average  temp,  of  vaporization  ; 
Ct  =  extra  coal  burned  per  hr.  on  account  of  wet 

shaft ; 

/  =  constants  determined  by  Regnault's  experi- 

0.305  rent; 

0.4805  —  sp.  heat  of  aq.  vapor  (see  Table  IV,  App.). 
Then  we  have  Regnault's  expressions  for 

Heat  of  vaporization  ....  w(  1 082  +  0.3054) 
Heat  absorbed  by  vapor 0.4805^,  —  *„) 

These  two  expressions  represent  the  total  heat  ren- 
dered latent  by  the  formation  of  the  vapor  and  the 
raising  of  the  temperature  of  that  vapor  to  the  tem- 
perature of  the  shaft.  Adding  these  together  and 
dividing  by  the  thermal  units  in  a  pound  of  coal,  we 


ECONOMIC   DISCUSSION   OF  THE   FURNACE.         59 

find  an  expression  for  the  extra  coal  required  per  hour, 
on  account  of  the  wet  condition  of  the  shaft : 


0.4805(^1  ~  *,)  /YT  ,A 


14000 

The  total  coal  required  in  wet  shafts  is  the  sum  of 
equations  (XLIV)  and  (XLV). 

Cooling  Effect  of  Shafts.  —  Referring  again  to  the 
"  third  determination  "  in  the  practical  problem  in  the 
fore  part  of  this  chapter,  we  observe  that  it  is  there  re- 
quired to  ascertain  the  temperature  of  the  bottom  of 
the  upcast  current  when  we  know  the  average  tem- 
perature of  the  shaft  ;  or,  in  other  words,  when  we 
know  what  the  average  temperature  of  our  upcast  shaft 
must  be,  in  order  to  produce  a  certain  ventilating  cur- 
rent, we  are  hereby  enabled  to  establish  therefrom  the 
necessary  temperature  at  the  furnace.  This  determina- 
tion depends  upon  a  certain  empirical  coefficient  of 
cooling  /£,,  based  upon  the  principle  that  one  square 
foot  of  the  inner  surface  of  the  shaft  possesses  a  certain 
cooling  power  or  conductivity  of  the  heat  of  the  cur- 
rent, by  which  a  definite  number  of  units  of  heat  are 
carried  off  per  minute  from  the  volume  of  air  passing. 

Expression  for  Coefficient  of  Cooling.  —  It  is  ob- 
vious that  the  loss  of  heat,  or  fall  in  the  temperature  of 
the  upcast  current,  in  different  shafts  is  proportionate 
to  the  exposed  cooling  surfaces  of  the  respective  shafts, 
and  inversely  proportionate  to  the  weight  of  air  pass- 
ing; hence  assume  the  following: 

o  =  perimeter  of  the  shaft  ; 
d  =  depth  of  the  shaft  ; 


60  MINE-VENTILATION. 

Q  =  quant,  of  air  passing  per  min.,  at  any  temp,  (t). 
W  =  weight  of  air  passing  per  minute. 
L  =  loss  of  heat  or  fall  in  temp,  of  the  current  in  pass- 

ing from  the  bottom  to  the  top  of  the  shaft  ; 
k^  =  relative  coefficient  of  cooling. 

And  from  what  has  preceded  we  have  the  following 
compound  proportion,  remembering  that  the  cooling 
surface  of  the  shaft  is  indicated  by  (do),  and  represent- 
ing the  like  quantities  in  another  shaft  by  the  same 
symbols  primed  : 


_ 

"  W 


But,  referring  to  equation  (XLIII),  we  may  write  the 
proportion 


.        .. 
'-459+<," 


w.w. 
^• 

Combining  these  two  proportions,  we  have 

^(459  +  /)  ,  fo,(459  +  *.) 
'" 


From  this  last  proportion,  (3),  we  may  write  the  equa- 
tion 

QJB.L,  QBL 


^(459  +  ')' 


(4) 


Now,  as  we  are  in  search  of  an  empirical  formula, 
the  first  member  of  equation  (4)  (containing  all  the 
quantities  referring  to  one  shaft)  is  determined  by  ex- 
periment, and  its  value  denoted  by  kr  Experiments 
should  be  performed  upon  several  shafts,  and  the  re- 


ECONOMIC   DISCUSSION   OF  THE  FURNACE.        6l 

suits  averaged,  to  obtain  a  reliable  value  for  this  co- 
efficient of  cooling.  Substituting  £,  for  the  first  mem- 
ber of  equation  (4),  above,  we  have 

QBL  (5) 


Again,  solving  with  respect  to  Z,  and  replacing  t  by  tv 
our  assumed  temperature  relative  to  the  quantity  Q, 
we  have 

L=—$B-^ ^ 

But  it  is  obvious  at  once  that 

£  =  2(*.-0; (7) 

hence,  combining  these  last  two  equations,  (6)  and  (7), 
and  solving  with  respect  to  /B,  we  have,  finally, 


This  coefficient  (^)  is  relative,  having,  as  we  have 
said,  an  empirical  value  which  represents  in  degrees  the 
amount  of  cooling  of  one  cubic  foot  of  the  upcast  cur- 
rent due  to  one  square  foot  of  the  inner  or  cooling  sur- 
face of  the  shaft.  No  reliable  determination  of  its 
value  has  as  yet  been  made.  We  assumed  previously, 
in  our  practical  problem  in  the  fore  part  of  the  chapter, 
that  this  coefficient  had  a  value  of  0.5  degree,  which 
is  more  or  less  approximate. 


62  MINE-VENTILATION. 


CHAPTER  VIII. 

ECONOMIC  DISCUSSION  OF  THE  FAN. 

Prefatory. — As  remarked  in  the  previous  chapter  in 
regard  to  the  furnace,  this  discussion  will  treat  of  the 
construction  of  the  fan  only  as  such  construction 
affects  its  efficiency  as  a  ventilating-machine.  We  will 
take  up  in  their  order  the  essential  or  vital  points  re- 
lating to  fans  and  fan  construction,  a  thorough  under- 
standing of  which  is  necessary  before  perfect  designing 
and  constructing  can  be  attained. 

Efficiency. — We  will  begin  with  efficiency.  Much 
depends  upon  the  efficiency  of  a  fan.  Some  fans  work 
better  than  others,  on  account  of  the  details  of  their 
construction  being  more  perfect :  they  have  been  better 
made ;  better  mechanics  have  worked  upon  them. 
Some  types  of  fans  work  better  than  others  on  account 
of  better  designing:  they  have  been  constructed  upon 
a  better  principle.  The  term  "  Efficiency,"  as  applied 
to  a  fan,  is  a  termin  dicating  the  ratio  existing  or 
inherent  in  that  fan  between  the  theoretical  and  the 
practical  work  such  fan  is  capable  of  performing.  Thus 
if  we  say  a  certain  fan  has  an  efficiency  of  90$,  we 
mean  that  on  account  of  internal  friction  or  defective 
construction,  or  some  other  cause,  known  or  unknown, 
that  particular  fan  will  only  perform  90$  of  its  theoreti- 
cal work  ;  we  do  not  mean  that  the  fan  will  only  supply 
90$  of  the  theoretical  quantity  of  air,  nor  do  we  mean 
that  it  will  only  yield  90$  of  the  theoretical  depression 


ECONOMIC    DISCUSSION   OF   THE    FAN.  63 

or  water-gauge,  but  its  practical  or  effective  work,  de- 
noted by  U,  will  be  90$  of  its  theoretical  work,  £7,. 

Coefficient  of  Efficiency.  —  Denoting  this  coefficient 
of  efficiency  by  K  ,  as  in  Chapter  VI,  we  write 

U=K{Ul),    ......    (i) 

or 


How  Varies.  —  We  see  then,  from  what  precedes,  that 
the  simple  passage  of  a  current  of  air  through  a  fan  re- 
quires a  certain  amount  of  work,  owing  to  the  resistance 
offered  by  the  fan  to  the  flowing  air.  This  work  is  prac- 
tically lost  or  absorbed  in  the  fan  ;  the  balance  of  the 
work,  which  is  applied  to  the  movement  of  the  air-cur- 
rent through  the  mine,  is  called  the  Effective  work. 
It  is  obvious,  then,  that  the  efficiency  of  a  fan  depends 
upon  the  amount  of  work  thus  absorbed  by  the  fan 
and  lost.  Let  us  now  investigate  a  step  further,  and 
ascertain  upon  what  the  coefficient  of  efficiency  de- 
pends, and  whether  or  not  it  is  a  constant  for  the  same 
fan  running  at  all  speeds.  We  observe  at  once  — 

First,  the  work  of  the  fan  lost  within  itself  is  due 
wholly  to  the  resistance  encountered  by  the  air  in  its 
passage  through  the  fan,  whether  such  resistance  is 
owing  to  defective  construction  or  other  cause  whatso- 
ever. 

Second,  that  this  resistance  varies  as  the  inner  rub- 
bing-surface of  the  fan  and  the  square  of  the  accelera- 
tive  *  velocity,  and  material  obstructions  common  to 

*  The  accelerative  velocity  is  taken  as  creative  of  the  internal  resist- 
ance, for  the  reason  that  the  accelerative  velocity  is  the  measure  of 


64  MINE-VENTILATION. 

fan-construction  ;  but  for  any  one  fan  in  question  the 
rubbing-surface  of  the  fan  and  other  material  obstruc- 
tions are  constant,  and  the  internal  resistance  of  that 
fan  will  vary  as  the  square  of  the  accelerative  velocity 
only. 

Internal  Resistance  of  a  Fan.  —  We  may  therefore 
represent  the  internal  resistance  of  a  fan  by  the  ex- 
pression £2/2,  >£2  being  a  constant  factor  expressive 
of  the  resistance  of  that  particular  fan  to  an  air-current 
having  a  unit  of  accelerative  velocity. 

Work  of  the  Resistance.  —  The  work  of  this  resist- 
ance is  clearly  the  work  lost  in  the  fan,  its  expression 
being   ^3/3,    in  which   kz  is  a  new  constant.      Assume 
u  —  the  effective  work  of  the  fan  for  a  unit  of  time  ; 
H!=  the  expended  work  of  the  fan  for  a  unit  of  time  ; 
u^=.  the  work  lost  or  absorbed  in  the  fan  in  a  unit  of 
time. 

Now,  referring  to  equation  (6-XXXVIII)  we  see  that 
f  varies  as  n*  ;  hence  from  what  precedes  we  may 
write,  for  the  work  lost  or  absorbed  in  the  fan, 


(3) 


The  coefficients  k^  ,  k^  ,  ki  are  merely  general  coefficients. 

N.B.  —  We  must  note  here,  that  the  work  lost  in  the 
fan  is  dependent  alone  upon  the  acceleration  f  due 
to  the  mechanical  velocity  of  the  fan,  and  is  in  no  way 
affected  by  changes  in  temperature  or  barometric  pres- 
sure, as  is  the  effective  work  of  the  fan. 

General  Expression  for  the  Work  of  the  Fan.  — 

the  force  created  within  the  motor  where  the  resistance  is  developed  ; 
and  it  is  this  active,  energizing  force  within  the  motor  that  is  produc- 
tive of  the  resistance  to  the  passage  of  the  current  through  that  motor. 


ECONOMIC   DISCUSSION   OF  THE   FAN.  65 

Referring  now  to  equation  (lO-XXXVIII),  which  ex- 
presses the  total  expended  work  for  one  second  of  time, 
we  see  that  for  any  one  fan  the  total  expended  or  theo- 
retical work  of  that  fan  is  dependent  upon  three  vari- 
ables, viz.,  speed  of  fan,  temperature,  and  barometer. 
We  may  therefore  write  for  that  equation  the  general 
equation 


in  which  c  is  a  constant  for  any  one  fan.  But  as  the 
effective  work  is  always  equal  to  the  total  expended 
work,  minus  the  work  lost,  we  have 


(5) 


Substituting  for  «,  and  ?/, ,  in  equation  (5),  above,  their 
respective  values  as  taken  from  equations  (3)  and  (4), 
above,  we  have  for  the  general  equation  for  the  effective 
work 

4  &  78  (£\ 

u  =  cn •  —k.n (6) 

459  +  ' 

Value  of  K. — But  the  value  of  K,  (see  equation  (2), 
above)  is  found  by  dividing  the  effective  work  by  the 
total  expended  work ;  hence,  dividing  equation  (6)  by 
equation  (4),  above,  member,  by  member  and  reducing, 
substituting  K  for  its  value,  we  have,  finally, 


(XLVII) 


in  which  <ra  is  a  new  constant,  which  we  term  the  fan 
constant,  as  explained    later.      Thus   we   see   that   the 


66  MINE-VENTILATION. 

coefficient  of  efficiency  K  is  not  a  constant,  but  varies 
with  the  speed  and  with  the  temperature  and  baromet- 
ric pressure,  but  not  in  the  same  proportion. 

Relative  Efficiency  at  Different  Speeds. — Let  us 
investigate  further,  and  ascertain  what  effect  the  speed 
of  the  fan  will  have  with  reference  to  a  maximum  and 
a  minimum  yield.  It  is  interesting  to  note  in  this  con- 
nection, that  if  a  fan  has  an  efficiency  of  95^  at  a  speed 
of  50  revolutions  per  minute  the  efficiency  of  the  same 
fan,  at  a  speed  of  100  revolutions  per  minute  will  only 
be  80$,  the  temperature  and  barometric  pressure  re- 
maining the  same.  If  the  efficiency  is  90$  at  a  speed 
of  50  revolutions  per  minute,  the  same  fan  working 
under  the  same  conditions  of  temperature  and  baromet- 
ric pressure  will  only  present  an  efficiency  of  6of0  at  a 
speed  of  100  revolutions  per  minute.  We  note  also, 
from  an  inspection  of  equation  (XLVII),  that  for  the 
same  speed  the  efficiency  of  a  fan  will  vary  as  the  ex- 
pression 459-}-/  varies,  and  inversely  as  the  baromet- 
ric pressure,  but  not  in  the  same  proportion. 

Limit  of  Speed.— We  see,  from  a  further  inspection 
of  equation  (XLVII),  that  the  value  of  K  will  become 
zero  when 

-t 


or  when 

-....     (XLVIII) 


This  last  equation  gives  the  limit  of  speed  for  the  fan 
in  question,  or  the  speed  at  which  that  particular  fan 
will  cease  to  deliver  any  air.  We  must  remember, 


ECONOMIC    DISCUSSION   OF   THE   FAN.  67 

however,  that  the  quantity  c^  has  a  particular  value 
for  every  fan,  according  as  the  fan  is  more  or  less  effi- 
cient in  its  work.  This  will  be  explained  later. 

Maximum  Effective  Speed..  —  Let  us  now  deter- 
mine the  maximum  effective  speed,  or  the  speed  at 
which  any  particular  fan  will  throw  its  maximum  of 
air  at  a  certain  temperature  and  barometric  pressure. 
Referring  to  equation  (XXXIX),  and  substituting  for 
K  its  value  as  taken  from  equation  (XLVII),  we  ob- 
serve that  Q  will  have  a  maximum  value  for  any  par- 
ticular fan  forcing  air  into  any  particular  mine,  when 
the  expression 


is  a  maximum  ;  or,  as  this  expression  may  be  written, 


In  expression  (2),  n  represents  any  possible  velocity  or 
speed  of  the  fan.  Now,  denoting  the  next  consecutive 
velocity  or  speed  by  n  +  I,  we  have  for  the  corre- 
sponding expression,  relative  to  the  speed  n-\-  I, 


(3) 


Let  us  analyze  these  three  expressions  carefully.  From 
expression  (i),  we  see  that  the  quantity  yielded  by  any 
fan  depends  upon  two  variable  factors,  relative  to  the 
speed  of  the  fan  :  the  first  a  direct  factor,  increasing  as 
the  speed  increases  ;  the  second  an  inverse  factor,  de- 
creasing as  the  speed  increases  (not,  however,  in  the 


68 


MINE-VENTILATION. 


same  proportion).  The  first  of  these  two  factors  repre- 
sents simply  the  speed  of  the  fan ;  while  the  second,  as 
we  have  seen  from  equation  (XLVII),  represents  the 
efficiency,  which  continues  to  decrease  as  the  speed  in- 
creases. 


Origin 


FIG.  IV. 

Fig.  IV  represents  graphically  the  relation  existing 
between  the  power,  speed,  and  efficiency  of  a  fan. 

Expressions  (2)and  (3)  are  expressions  relative  to  quan- 
tity for  any  two  consecutive  states  of  speed  of  the  fan. 
Examining  expression  (2),  we  see  that  its  value  increases 
as  n  increases,  but  not  in  the  same  proportion,  the 
rate  of  increase  being  less  and  less  as  the  velocity  is 
higher.  For  this  reason,  as  we  increase  the  speed  by 
one,  the  resulting  increase  of  quantity  for  each  consec- 
utive state  will  be  less  and  less,  till  finally  there  ceases 
to  be  any  increase  of  quantity  for  an  increase  of  speed. 
Previous  to  this  juncture  the  value  of  expression  (3)  has 
been  greater  than  the  value  of  expression  (2),  but  it 
now  becomes  equal  to  it ;  and  if  the  speed  be  in- 
creased beyond  this  point  the  value  of  expression  (3) 
will  become  less  than  that  of  expression  (2) :  that  is  to 


ECONOMIC   DISCUSSION   OF   THE   FAN.  69 

say,  the  quantity  of  air  will  diminish  from  this  point 
until  it  fails  altogether,  as  shown  by  equation  (XLVIII). 
Hence  it  is  obvious  that  to  determine  that  value  for 
n  which  will  give  the  maximum  quantity  of  air,  we 
must  equate  expressions  (2)  and  (3),  which  will  give, 
after  reducing, 

(«  +  O4  -  "4  _  r  459+*  ,XT  TXx 

••-'•—  - 


This  is  the  simplest  form  of  this  equation  obtainable  : 
it  means  that  the  difference  between  the  fourth  powers 
of  two  consecutive  speeds  of  the  fan,  at  the  point  of 
its  maximum  yield,  divided  by  the  difference  between 
the  sixth  powers  of  the  same  speeds,  will  be  equal  to 
the  expression  given  in  the  second  member  of  the 
equation.  These  are  important  formulas,  and  reveal  the 
true  action  of  the  fan  ;  they  should  be  understood  by 
all  who  are  interested  in  the  question  of  scientific  fan- 
construction.  They  show  that  it  is  of  no  avail  to  speed 
a  fan  beyond  its  maximum  effective  speed  ;  and  it  is, 
moreover,  a  profligate  waste  of  power,  the  power  being 
proportionate  to  the  fourth  power  of  the  speed  (see 
eq.  (lO-XXXVIII)  ;  and  for  this  expenditure  of 
power  we  obtain  less  air  than  at  a  lower  speed. 

To  determine  Value  of  K,  practically.—  This  de- 
termination should  be  made  in  the  shop  for  each  type 
of  fan  made.  The  best  method  is  to  set  the  fan  up,  as 
will  be  described  later  in  this  chapter  under  "  Testing 
a  Fan  "  ;  and  having  carefully  noted  the  quantity  and 
pressure  at  a  speed  of,  say,  50  revolutions  per  minute, 
increase  this  speed  to  75  revolutions  per  minute,  and 
note  the  quantity  and  pressure  again  ;  repeat  the  same 


/O  .         MINE-VENTILATION. 

at  a  speed  of  100  revolutions  per  minute.  Now  by 
referring  to  equation  (XII)  we  see  that  the  product  of 
these  two  factors  will  give  the  work — in  this  case  the 
effective  work  (the  observations  being  taken  at  the 
point  of  application)  ;  hence,  substituting  these  several 
products  successively  for  £/,  in  equation  (XXXVIII) 
and  solving  with  respect  to  K,  we  obtain  the  value  of 
K  for  each  of  these  speeds,  respectively.  The  tem- 
perature and  barometric  pressure  must  be  noted  in 
these  observations,  and  substituted  in  the  equation  at 
the  same  time.  This  will  give  the  value  of  K  for 
certain  speeds  of  the  fan  and  under  certain  atmospheric 
conditions. 

Value  of  the  Fan  Constant. — Referring  to  equation 
(XLVII),  and  substituting  therein  successively  the  sev- 
eral values  found  for  K  and  the  corresponding  values  of 
«,  together  with  the  noted  temperature  and  baromet- 
ric pressure,  and  solving  with  respect  to  <ra,  we  ob- 
tain the  value  of  this  constant,  which  we  call  the  "  Fan 
Constant,  "  because  it  has  a  constant  value,  peculiar  to 
any  one  fan  in  question.  Knowing  the  value  of  this 
constant,  the  efficiency  of  the  fan  at  any  speed  of  the 
fan  may  be  determined  by  substitution  in  equation 
(XLVII). 

Effect  of  Humidity. — There  is  one  other  factor  which 
affects  not  only  the  efficiency  of  a  fan,  but  also  its  ini- 
tial work,  as  expressed  by  equation  (XXXVIII).  This 
factor  is  the  humidity  of  the  atmosphere,  or,  as  we 
say,  its  "  hygrometric  state."  Its  effect  is  small,  and 
for  all  practical  purposes  may  be  ignored  ;  nevertheless, 
as  a  matter  of  information,  it  is  well  to  refer  to  it.  The 
quantity  of  air  a  fan  will  yield,  as  expressed  by  equa- 


3TNIVERSITY 

ECONOMIC   DISCUSSION 


tion  (XXXIX)  varies  with  the  cube  root  of  the  expres- 
sion 


(i) 


The  coefficient  of  efficiency  K  depends  for  its  value 
upon  the  reciprocal  of  the  same  expression.  This  ex- 
pression is  taken  from  equation  (I),  and  relates  to  the 
weight  of  dry  air.  Now  if  we  write  equation  (I)  so  as 
to  express  exactly  the  weight  of  a  cubic  foot  of  air  sat- 
urated with  aqueous  vapor,  we  should  have 


=  _ 


459 


in  which  0  is  the  tension  of  the  vapor  of  saturation 
at  the  temperature  t  (see  Table  III  of  the  Appendix), 
the  specific  gravity  of  aqueous  vapor,  referred  to  air  of 
the  same  temperature,  being  0.6235  (see  Table  V  of  the 
Appendix).  Since  this  effect  is  so  small,  we  do  not  bur- 
den our  equations  with  its  expression  ;  but,  for  the 
matter  of  information,  we  have  prepared  Tables  VIII 
and  IX  of  the  Appendix,  showing  the  effect  atmos- 
pheric changes  have  upon  the  quantity  of  air  delivered 
by  a  fan,  the  speed  being  maintained  constant  (Table 
VI  IJ),  and  the  effect  of  the  same  upon  the  speed  when 
the  power  applied  remains  constant  (Table  IX).  We 
see  from  Table  VIII  that  the  effect  of  complete  satu- 
ration at  a  temperature  of  60°  F.  amounts  to  about 
0.25$  of  the  yield,  while  at  90°  F.  it  amounts  to  about 
0.55$.  That  is  to  say,  if  a  fan  is  throwing  100,000 
cubic  feet  of  dry  air  at  90°  F.,  it  would  throw  at  the 
same  speed  and  temperature  99,450  cubic  feet  of  air 


72  MINE-VENTILATION. 

fully  saturated  with  aqueous  vapor,  against  the  same 
mine-potential. 

Resume. — We  have  thus  far  discussed  the  efficienc}' 
of  a  fan,  showing  upon  what  it  depends,  how  it  varies^ 
and  how  it  is  affected  by  atmospheric  conditions  ;  refer- 
ring incidentally  to  the  effect  of  the  same  upon  the  in- 
itial work  of  the  fan.  Let  us  now  take  a  step  further 
and  consider  some  factors  or  elements  in  the  construc- 
tion of  the  fan,  as  bearing  upon  its  yield. 

Outer  Radius  or  Diameter.— The  distinctive  di- 
mension of  a  fan  is  its  diameter.  We  speak  of  a  fan 
in  terms  of  its  diameter — as,  for  example,  a  lo-foot  fan 
or  a  2O-foot  fan ;  and  this  is  proper,  as  the  radius  or 
diameter  more  than  any  other  dimension  symbolizes 
the  power  and  determines  the  comparative  importance 
of  the  fan  as  a  ventilating  motor.  As  different  styles  of 
fans  are  adapted  to  different  kinds  of  work,  so  the  vari- 
ous dimensions  of  a  fan  have  each  their  respective 
functions  and  adaptability  to  certain  portions  of  the 
work.  We  may  have  a  small  volume  of  air  to  pass 
through  a  long  or  contracted  airway ;  or  we  may  have 
a  large  volume  of  air  to  circulate  through  short,  ex- 
panded airways :  in  each  of  these  cases  the  necessary 
power  may  be  the  same,  but  the  kind  of  work  and  the 
style  of  motor  best  adapted  to  perform  the  work  in 
each  case  are  very  different.  Referring  to  equation 
(XX  VI 1 1),  we  may  call  it  the  elemental  equation  of  power; 
because  it  represents  the  two  elementary  factors  of 
ventilation  which  absorb  the  power.  These  two  ele- 
mentary factors  of  ventilation,  quantity  of  air  passing, 
and  mine-potential  against  which  it 'Is  passing,  have  their 
representative  adjuncts  in  the  several  dimensions  of  the 
fan.  The  diameter  of  the  fan  is  the  counterpart  or  repre- 


ECONOMIC   DISCUSSION   OF   THE   FAN.  73 

sentative  of  the  mine -potential;  and  the  fan  whose  diame- 
ter is  thus  proportioned  to  this  factor  of  its  work  is  best 
adapted  to  do  its  work,  and  will  yield  the  best  results. 
This  will  be  explained  fully  under  General  Proportion- 
ment  of  the  Fan. 

Inner  Radius  or  Size  of  Eye. — This  dimension  of 
the  fan  is  most  important,  as  determining  the  area  of 
the  eye  or  the  size  of  the  inlet  of  the  fan  ;  and  as  such  it 
is  the  representative  of  the  quantity  of  air  passing.  It 
should,  beyond  a  doubt,  be  proportioned  to  this  factor. 
The  size  of  this  opening  should  be  such  as  to  accom- 
modate the  quantity  of  air  the  fan  will  be  required  to 
throw,  at  a  velocity  not  greater  than -from  16  to  20  feet 
per  second.  In  figuring  upon  this  area  it  must  be  re- 
membered that  the  unobstructed  area  of  the  two  eyes 
is  referred  to  as  the  inlet  area. 

Number  of  Blades. — The  number  of  fan-blades  is 
somewhat  dependent  upon  the  size  of  the  fan.  There 
should  be  as  few  blades  as  is  consistent  with  keeping 
the  contained  air  pressed  forward.  For  all  ordinary 
sizes  eight  blades  make  a  good  number,  but  when  the 
distance  between  the  blade  tips  exceeds  ten  or  twelve 
feet  we  should  begin  to  increase  the  number  of  the 
blades.  In  order  to  reap  the  best  results,  the  air  at 
the  circumference  should  not  be  left  unsupported.  A 
good  plan  is  to  introduce  small  or  secondary  blades  at 
the  circumference  of  the  fan,  running  inward  only  half 
as  far  as  the  other  blades  ;  the  air  is  thus  supported  at 
the  circumference  and  the  friction  at  the  inlet  is  not 
materially  augmented. 

Width  of  Blade. — This  is  a  most  important  dimen- 
sion of  the  fan,  although  one  which  has  been  ignored 
by  writers.  Why  this  is  so  is  hard  to  understand. 


74  MINE-VENTILATION. 

It  is  possible  that  this  omission  occurs  from  the  failure 
to  distinguish  between  static  and  dynamic  pressure,  as 
in  static  pressure  the  width  of  the  fan-blade  divides 
out  (see  Chapter  II.).  This  dimension  of  the  fan  is  the 
representative  of  the  quantity,  as  the  diameter  is  the 
representative  of  the  mine-potential :  it  should  be  pro- 
portioned to  the  quantity  of  air  the  fan  is  expected  to 
pass  per  minute.  As  we  have  previously  stated  in  the 
introductory  chapter,  a  high  mine-potential  always  indi- 
cates a  large  quantity  of  air  moving  at  a  comparatively 
small  expenditure  of  power ;  and  this  condition  always 
obtains  when  several  splits  are  made  in  the  air-current. 
The  typical  fan,  under  such  conditions,  should  have 
short,  broad  blades.  In  fact,  however,  it  is  possible, 
by  the  adoption  of  a  judicious  system  of  ventilation, 
and  by  splitting  the  air  from  time  to  time  as  the  mine 
becomes  more  extended,  to  4 maintain  the  elemental 
equation  of  power  referred  to  above  (eq.  XXVIII)  at 
about  a  constant  value.  This  should  be  done,  and 
a  fan  employed  having  a  less  diameter  and  broader 
blades.  This  type  of  construction  will  be  seen  to  pos- 
sess a  mechanical  advantage  also,  by  giving  better  op- 
portunity for  swray-bracing,  and  will  make  a  stronger 
fan.  Such  a  fan,  under  the  conditions  stated,  will  be 
adapted  to  its  work, 

Curvature  of  Blades. — Another  point  with  reference 
to  the  blades  of  the  fan  is  the  form  of  blade  that  will 
yield  the  greatest  efficiency,  or  transmit  the  greatest 
percent  of  the  power  applied.  This  is  a  question  which 
has  from  time  to  time  given  rise  to  considerable  differ- 
ence of  opinion,  some  maintaining  that  the  blades  when 
curved  backward  from  the  direction  of  the  motion  was 
best  adapted  to  propel  the  air.  We  believe  there  is 


ECONOMIC   DISCUSSION   OF  THE   FAN. 


75 


but  one  solution  to  the  question  :  we  give  our  ver- 
dict in  favor  of  the  straight-paddle  blade-,  except  as  the 
inner  edge  of  each  blade  should  be  curved  forward  in 
the  direction  of  the  motion ;  the  idea  of  the  forward 
curvature  of  the  inner  edge  of  each  blade  being  to  con- 
vert the  radial  motion  of  the  incoming  air  into  the 
enforced  rotary  motion  of  the  fan-blades,  with  as  lit- 
tle shock  as  possible.  There  is  always  absorp- 
tion of  power  in  lost  motion  or  shock ;  and  any  de- 
vice by  which  this  is  avoided,  by  deflecting  the 
course  of  the  current  into  its  proper  channels  without 
shock,  is  an  assistance :  it  will  show  in  the  increased 


FIG.  V. 


FIG.  VI. 


efficiency  of  the  fan.  A  conical  arrangement  about  the 
shaft,  whereby  the  incoming  current  would  be  deflected 
radially,  as  shown  in  Fig.  V,  would  be  beneficial  in 
cases  where  the  fan  is  crowded,  or  where  the  intake  is 
at  a  high  velocity ;  in  general,  however,  this  arrange- 
ment is  unnecessary,  as  the  intake-chamber  of  the  fan 
should  be  large,  and  the  velocity  at  this  point  thereby 
reduced  to  a  minimum.  Before  leaving  the  discussion 
of  blades,  let  us  look  for  a  moment  at  the  "  Murphy" 
fan,  represented  in  Fig.  VI.  The  characteristic  of  this 


76  MINE-VENTILATION. 

fan  is  the  curved  blade :  the  fan  gives  fair  results,  and 
has  many  advocates;  but  we  believe  that  this  type  of 
construction  will  consume  a  greater  amount  of  power, 
in  proportion  to  the  yield,  than  the  straight-paddle  fan. 
The  main  point  of  difference  between  these  two  types, 
with  reference  to  their  working,  is  the  speed :  working 
under  the  same  conditions  and  delivering  the  same 
amount  of  air,  the  speed  of  the  Murphy  fan  is  much 
the  greater  of  the  two.  The  Murphy  fan  is  in  some 
sense  a  screw-motor,  and  as  such  differs  essentially 
from  the  straight-paddle  fan  in  its  working  principle. 
Certain  it  is  that  some  of  the  air  is  carried  around  by 
the  revolving  blades  and  expelled  by  virtue  of  the  cen- 
trifugal force  thus  developed  :  the  amount  of  air  thus 
contributing  to  a  centrifugal  pressure  will  vary  accord- 
ing to  the  greater  or  less  inclination  of  the  blades  ;  the 
blades  could  be  so  wreathed  into  a  spiral  as  to  convert 
the  fan  wholly  into  a  screw-machine,  when  its  action 
would  cease  to  be  anything  other  than  mechanical ;  and 
its  necessary  speed  would  have  to  be  enormous  in  order 
to  compete  as  an  air-motor.  The  reasoning  that  would 
lead  some  to  adopt  a  curved  blade  is  to  establish  as  lit- 
tle friction  as  possible  between  the  radial  passage  of 
the  air  through  the  fan  and  the  rotary  motion  of  the 
blades ;  but  we  must  remember  that  whatever  tends  to 
decrease  the  rotary  motion  of  the  air  in  the  fan  will 
decrease  in  the  same  proportion  the  efficiency  or 
transmitting  power  of  the  fan,  because  the  less  the  air 
is  revolved  the  less  will  be  the  centrifugal  force  devel- 
oped. The  equations  developed  in  Chapter  VI  giving 
the  work,  yield,  and  horse-power  of  straight  paddle  fans, 
do  not  apply  to  fans  having  curved  or  inclined  blades. 
(See  Addenda.) 


ECONOMIC   DISCUSSION   OF   THE   FAN.  JJ 

Expansion  of  Casing. — The  peripheral  expansion 
of  the  fan  casing  is  another  important  point  in  the  eco- 
nomic construction  of  the  fan.  The  reason  for  such 
expansion  is  simple  and  obvious.  Each  section  of  the 
fan  is  supplying  its  quota  of  air  to  the  conduit  or  shaft 
leading  to  the  mine  ;  and  the  effective  power  of  the 
fan  depends  upon  the  continual  and  free  passage  of  the 
air  through  these  several  compartments  or  sections  and 
thence  to  the  mine,  the  moving  force  behind  the  cur- 
rent, being  the  combined  pressure  from  all  of  these  com- 
partments. Now  if  the  connection  of  these  compart- 
ments with  the  airways  of  the  mine  is  cut  off  during  a 
portion  of  their  revolution  by  a  tight  casing,  their  ac- 
tion ceases  for  such  time,  and  the  power  of  the  fan  is 
diminished.  On  the  other  hand,  if  the  peripheral  cas- 
ing be  regularly  expanded  from  a  point  near  the  cut- 
off, around  the  entire  circumference  of  the  fan,  to  the 
cut-off  again,  there  will  be  provided  thereby  a  gradual 
increase  of  the  sectional  area  of  the  peripheral  space, 
equal  to  the  augmentation  of  the  flow  from  each  com- 
partment;  consequently  there  will  be  established  a 
peripheral  flow  of  air  about  the  fan  and  past  the  cut-off, 
having  a  constant  velocity.  That  is  to  say,  the  veloc- 
ity of  this  peripheral  flow  will  be  the  same  at  any  point 
of  the  circumference  of  the  fan,  and  may  be  determined 
by  dividing  the  area  of  the  cut-off  by  the  entire  flow. 
The  amount  of  this  expansion  e  (see  Fig.  VII),  mul- 
tiplied by  the  width  of  the  fan-blades  b,  will  give  the 
area  of  expansion.  This  area  of  expansion  should  be 
large  enough  to  accommodate  the  flow  of  the  air-cur- 
rent at  a  velocity  proportionate  to  the  peripheral  veloc- 
ity of  the  fan.  We  say  that  the  velocity  of  the  current 
in  the  peripheral  space  should  be  proportionate  to  the 


78  MINE-VENTILATION. 

velocity  of  the  blade  tips,  for  the  reason  that  better 
results  will  be  obtained  if  the  air  travels  with  the  fan 
through  this  space.  If  necessary,  however,  the  air  will 
travel  ahead  of  the  fan.  For  like  reasons  as  the  above, 
this  expansion  of  the  casing  should  not  be  too  large, 
and  the  air  left  to  travel  behind  the  fan.  It  is  better 
that  the  expansion  be  less  and  the  air  urged  to  travel 
ahead  of  the  fan  rather  than  behind  it,  as  in  the  lat- 


Down-cast 
Shafts 


FIG.  VII. 


ter  case  there  is  an  opportunity  given  to  baffle.  Now, 
having  explained  the  office  of  the  peripheral  space 
formed  by  the  expansion  of  the  fan  casing,  let  us  ascer- 
tain carefully  the  relation  and  proportion  this  expansion 
must  sustain  to  the  other  dimensions  of  the  fan.  It 
will  be  seen  more  clearly  later  that  this  expansion  e  is 
the  representative  and  the  counterpart  of  the  mine- 
potential  in  the  elemental  equation  (XXVIII),  and 


ECONOMIC   DISCUSSION   OF   THE   FAN.  79 

must  be  proportioned  to  this  factor  of  the  work.  This 
will  be  seen  readily  from  a  practical  problem.  For  ex- 
ample, from  Table  X  of  the  Appendix  we  see  that  a 
twelve-foot  fan,  in  order  to  circulate  25,000  cubic  feet 
of  air  per  minute  against  a  mine-potential  of  685.064, 
must  have  a  speed  of  33.7  revolutions  per  minute ; 
while  to  circulate  the  same  current  against  a  potential 
of  342.532,  the  same  fan,  working  under  the  same  at- 
mospheric conditions,  must  have  a  speed  of  58.0  revo- 
lutions per  minute.  In  each  of  these  cases  the  same 
amount  of  air  is  passing  through  the  area  of  expansion 
at  the  cut-off.  Now,  to  go  back  a  little,  we  see  that 
the  velocity  of  the  peripheral  flow  should  be  maintained 
as  nearly  as  possible  at  the  velocity  of  the  blade  tips, 
which  has  changed  very  materially  in  the  two  cases  ; 
hence,  the  same  amount  of  air  passing  in  each  case,  if 
we  would  vary  its  velocity  as  the  velocity  of  the  blade 
tips  vary,  we  must  vary  the  area  of  expansion  through 
which  the  current  flows ;  but  we  have  alread)*  propor- 
tioned one  factor  of  this  area  b  to  the  quantity  of  air 
passing,  and  the  other  factor  e  must  therefore  be  pro- 
portioned to  the  potential. 

General  Proportionment  of  the  Fan. — The  three 
distinctive  dimensions  of  the  fan  are  then,  as  we  have 
seen,  the  Outer  Radius,  Breadth  of  Blade,  and  Expan- 
sion of  Casing.  In  referring  to  these  elements  of  the 
motor  we  have  stated  in  a  general  way  the  elements  of 
the  work  to  which  each  corresponds  and  with  reference 
to  which  it  must  be  proportioned.  It  must  not  be  sup- 
posed, however,  that  this  proportionment  of  the  ele- 
ments of  the  motor  to  the  elements  of  the  work  is  a 
simple  proportioning  of  element  to  element.  It  will  be 
readily  seen  that  these  elements  so  relate  to  each  other 


80  MINE-VENTILATION. 

that  a  change  of  one  necessitates  a  change  of  all.  For 
example,  a  change  in  the  radius  of  a  fan  not  only  results 
in  a  change  of  power,  but  also  in  a  change  of  quantity ; 
and  the  change  in  quantity  necessitates  a  change  in  the 
breadth  of  blade,  which  again  affects  the  power.  The 
expansion  of  the  casing  is  likewise  affected  by  the 
change  of  the  radius.  We  propose  now,  for  the  benefit 
of  the  mechanic  interested  in  the  construction  of  fans, 
as  well  as  for  the  mine  operator  who  must  decide  upon 
the  size  of  fan  that  he  will  need  for  the  ventilation  of 
any  proposed  workings,  to  formulate  these  elements 
of  the  motor,  expressing  the  value  of  each  in  terms  of 
the  work. 

Let  us  have  then  and  retain  in  our  minds  a  clear  idea 
of  power  as  applied  to  the  accomplishment  of  a  certain 
work.  The  power  thus  applied  finds  expression  in 
terms,  factors  or  elements  of  the  work.  We  have  re- 
ferred to  equation  (XXVIII)  as  the  elemental  equation 
of  power. 

U=  ^3.     ...        (XXVIII) 

2\. 

The  second  member  of  this  equation  designates  the 
elements  of  the  work — a  quantity  of  air  Q  to  be  circu- 
lated against  a  mine-potential  X.  This  is  the  work  to 
be  accomplished,  and  these  are  the  elements  of  such 
work.  As  we  have  seen,  these  elements  of  the  work 
have  their  counterparts  or  representatives  in  the  motor; 
and  as  one  or  the  other  of  these  elements  is  increased 
or  diminished,  its  representative  part  in  the  motor  must 
be  varied,  that  the  motor  maybe  adapted  to  its  work. 
We  must  note  here  that  while  this  proportionment  of 
parts  will  adapt  a  certain  motor  to  a  certain  work, 
there  is  yet  another  factor  of  the  working  of  the  motor, 


ECONOMIC    DISCUSSION    OF  THE   FAN.  8l 

viz.,  its  speed,  that  will  enable  it  to  perform  a  different 
work,  to  which  it  will  be  alike  adapted. 

In  deciding  upon  what  size  and  type  of  fan  will  be 
needed  for  the  ventilation  of  any  proposed  workings, 
we  must  first  know  the  elements  of  the  work  ;  or,  in 
other  words,  we  must  decide  upon  the  quantity  of  air 
we  wish  to  put  in  circulation,  and  against  what  poten- 
tial (size  and  length  of  airways,  giving  the  resisting 
power  of  the  proposed  workings).  This  will  determine, 
according  to  the  above  elemental  equation,  the  power 
we  must  employ  in  terms  of  the  work.  Let  us  now 
find  an  elemental  equation  showing  the  relation  be- 
tween the  elements  of  the  work  and  the  elements  of 
the  motor.  Referring  to  equation  (XXXIX)  and  assum- 
ing a  value  for  the  inner  radius  R^  equal  to  f^,  which 
gives  an  approximate  value  for  R^  equal  to  %R,  and  the 
value  of  the  expression  R*—R*  becomes  approximately 
f  R3  :  these  factors  all  then  reducing  to  the  expression 
cR\  in  which  c  is  a  constant  ;  and  substituting  X  for  its 
value  and  assuming  constant  values  for  B,  say  30  inches, 
and  for  /,  say,  60°  F.,  we  may  write 


(LI) 


This  is  the  general  equation  for  the  yield  of  a  straight 
paddle-fan  under  fixed  atmospheric  conditions,  as  as- 
sumed. By  referring  now  to  Table  VII  of  the  Appen- 
dix, which  gives  the  horse-powers  developed  by  certain 
fans  at  certain  speeds  and  under  the  same  atmospheric 
conditions  as  those  which  we  have  assumed,  we  may 
ascertain  the  value  of  the  coefficient  c,  which  gives 

).  .     .     (LII) 


82  MINE-VENTILATION. 

By  combining  equations  (XXVIII),  (XXXV),  and  (LII), 
and  solving  with  respect  to  H.P.,  we  have 

H.P.  =  o.ooooooooo362(A^V).     (LIII) 

Equations  (LII)  and  (LIII)  are  general  equations,  giv- 
ing the  work  and  the  horse-power  of  a  fan  in  terms  of 
itself,  and  may  be  used  in  estimating  upon  the  size  of 
fan  needed  for  the  development  of  any  assumed  horse- 
power, or  to  circulate  any  desired  quantity  of  air  per 
minute  against  any  assumed  mine-potential.  Equation 
(LII)  is  the  desired  elemental  equation  expressing  the 
relation  that  should  exist  between  the  elements  of  the 
work  and  the  elements  of  the  motor,  including  the 
speed  of  the  same.  But  we  have  said  that  the  fan 
should  be  so  proportioned  that  the  velocity  of  the  pe- 
ripheral flow  shall  not  much  exceed  that  of  the  blade 
tips.  This  imposes  a  new  condition  upon  the  propor- 
tioning of  the  parts,  which  is  expressed  by  the  equation 


(i) 


in  which  e  is  the  expansion  of  the  casing  at  the  cut-off. 
(See  Fig.  VII.)  We  assume  a  value  for  e  equal  to  \R, 
as  we  have  shown  that  R  and  e  are  both  functions  of 
the  same  element  of  the  work;  and  equation  (i)  above 
then  becomes 

.....     (LIV) 


Combining  equations  (LII)  and  (LIV)  so  as  to  elimi- 
nate by  and  solving  with  respect  to  R,  we  have,  after  re- 
ducing, 


ECONOMIC   DISCUSSION   OF  THE  FAN.  83 

From  the  same  equations  we  have  in  like  manner,  for 
the  value  of  b, 

£  —  0.00000121  —  -~  —  .    .     .     (LVI) 

We  have  also,  as  previously  assumed,  for  the  expansion 
of  the  casing, 

e  =  o.$R  ......     (LVII) 

Now  as  equations  (LV)  and  (LVI)  express  the  values 
of  R  and  b  in  terms  of  a  work  performed  at  a  speed  n, 
the  values  of  these  elements  are  indeterminate  until 
we  have  decided  upon  what  grade  of  fan  to  employ  ;  or, 
in  other  words,  at  what  speed  of  the  fan  the  work  is  to 
be  accomplished.  There  are  different  grades  of  fans 
capable  of  performing  the  same  work  at  different 
speeds.  We  may  therefore  assume  such  a  value  for  n 
as  will  make  b  equal  to  f  of  R.  This  will  make  b  and 
R  sustain  such  a  relation  to  each  other  as  will  be  best 
adapted  to  the  passage  of  the  current  through  the  fan. 
Under  this  supposition,  combining  equations  (LV)  and 
(LVI)  and  solving  with  respect  to  n,  eliminating  R,  we 
have 


«  =  268.67  rp  .     .     (LVIII) 

In  using  equation  (LVIII)  we  must  first  approximate 
a  value  for  K,  which  will  then  give  an  approximate 
value  for  n.  From  this  value  of  n,  however,  the  true 
value  of  K  is  found  and  substituted  in  the  equation, 
which  will  then  give  the  true  value  of  n.  We  see  from 
equation  (LVIII)  that  to  maintain  the  best  proportion 
between  the  outer  radius  of  a  fan  and  the  breadth  of 


84  MINE-VENTILATION. 

the  fan  blades  necessitates  a  certain  speed  of  the  fan 
for  the  accomplishment  of  a  certain  work.  From  equa- 
tions (LV)  and  (LVI)  we  see  that  as  we  increase  this 
speed  for  any  one  work  we  obtain  a  smaller  radius  and  a 
greater  breadth  of  blade  ;  and  vice  versa.  It  is  there- 
fore possible  to  obtain  a  narrow  fan  of  large  diameter 
or  a  broad  fan  of  small  diameter  which  will  be  alike 
adapted  to  the  same  work.  But  when  the  breadth  of 
blade  is  taken  at  about  three  fourths  of  the  outer  ra- 
dius, the  air  will  pass  through  the  fan  with  less  shock 
and  less  internal  resistance.  These  last  four  equations 
are  important  in  fan  construction,  and  should  be  in  com- 
mon use  in  the  shop  and  at  the  mine.  As  we  have  seen, 
they  have  been  deduced  from  the  more  complicated 
formula  (XXXIX)  by  approximation,  and  are  only  in- 
tended to  be  used  in  estimating  upon  the  size  of  fan 
needed  for  proposed  workings,  and  in  the  construction 
of  the  same.  It  is  not  intended  to  convey  the  idea 
that  a  different-sized  fan  should  be  figured  for  every 
mine,  but  to  show  the  necessity  for  the  proper  propor- 
tioning of  parts,  and  the  adaptation  of  fans  of  different 
sizes  and  proportions  to  different  workings.  It  is  sel- 
dom advisable,  where  the  fan  is  working  fairly  well  and 
yielding  the  necessary  amount  of  air,  to  make  changes, 
although  such  changes  would  be  for  the  betterment  of 
the  fan  and  result  in  a  saving  of  power ;  but  where 
there  is  a  scarcity  of  air,  changes  may  often  be  made 
and  must  be  made  to  increase  the  supply.  In  con- 
structing a  new  fan,  however,  it  will  be  of  great  pecu- 
niary advantage  to  have  the  new  fan  adapted  to  its 
work.  Again,  if  we  cannot  build  a  new  fan,  we  can 
often,  by  changing  the  system  of  ventilation  below,  by 
splitting,  or  otherwise,  so  adapt  the  work  to  the  fan  in 


ECONOMIC   DISCUSSION   OF  THE  FAN.  85 

use  that  the  required  results  will  be  attained.  We 
often  see  a  fan  that  is  expected  to  throw  100,000  cubic 
feet  of  air  per  minute,  when  its  size  and  proportions 
would  barely  permit  the  passage  of  50,000  cubic  feet 
per  minute;  and  yet  the  operator  has  a  vague,  indefi- 
nite idea  that,  by  speeding  this  fan  up,  it  can  be  made 
to  throw  all  the  air  he  will  need  for  future  develop- 
ment :  and  perhaps  it  will  supply  all  the  air  he  will 
need,  if  he  knows  as  much  about  the  rest* of  the  mining 
business  as  he  does  about  fans. 

Connection  with  the  Downcast. — The  connection 
of  the  fan  with  the  downcast  shaft  requires  as  much 
care  as  the  construction  of  the  fan  itself.  We  have  de- 
termined, in  the  last  paragraph,  what  the  area  of  expan- 
sion, or  the  area  at  the  cut-off,  should  be :  from  this 
point  the  area  of  the  air-conduit  should  increase  uni- 
formly till  the  top  of  the  downcast  is  reached,  care 
being  taken  to  avoid  sharp  angles.  The  cut-off  itself 
should  be  a  sharp,  well-defined  line,  made  with  a  sheet 
of  boiler-plate  iron  bent  back  upon  itself,  and  forming, 
for  a  short  distance  on  either  side  of  the  cut-off,  a  lin- 
ing to  the  fan  casing  and  to  the  air-conduit,  as  shown 
in  Fig.  VII.  The  expansion  of  the  air-conduit  from 
beyond  the  cut-off  should  not  be  too  slow,  as  a  great 
deal  depends  upon  getting  the  air  quickly  away  from 
where  it  would  hamper  the  free  action  of  the  fan  ;  but 
its  expansion  must  be  regular,  and  changes  in  direction 
be  made  with  curved  surfaces,  as  the  occurrence  of 
angles  or  sudden  changes  in  the  sectional  area  of  the 
conduit  gives  rise  to  baffles  and  eddies.  The  periphe- 
ral casing  should  be  continued  tangentially  to  the  outer 
curve.  The  expansion  of  the  air-conduit  should  con- 
tinue till  its  sectional  area  is  equal  to  the  sectional  area 


86  MINE-VENTILATION. 

of  the  downcast  shaft.  This  downcast  area  should  be, 
properly,  twice  the  sectional  area  of  the  main  airways 
below,  and  the  air-course  leading  from  the  foot  of  the 
downcast  should  have  the  same  double  area,  until  the 
point  of  the  first  split  is  reached.  It  is  a  good  plan  to 
set  the  fan  as  far  over  the  mouth  of  the  downcast  shaft 
as  the  foundation  of  the  fan  will  permit.  Fig.  VII 
shows  the  general  arrangement  of  the  connection  with 
the  downcast  shaft. 

Testing  a  Fan  at  the  Shops. — The  proper  test  to 
apply  to  a  fan  at  the  shop  is  to  place  it  under  condi- 
tions as  nearly  similar  to  those  under  which  it  will  be 
compelled  to  work  at  the  mine,  as  it  is  possible  to  make 
them  ;  in  other  words,  to  cause  it  to  deliver  a  certain 
quantity  of  air  while  working  under  a  certain  pressure, 
and  then  making  all  the  observations  and  noting  them 
down  carefully,  as  described  earlier  in  this  chapter;  and 
from  these  observations  determining  the  value  of  the 
efficiency  and  of  the  fan  constant,  as  there  described. 
To  conduct  this  test,  which  when  once  done  will  answer 
for  all  fans  of  that  type  and  need  not  be  repeated  for 
each  particular  fan,  the  motor  is  set  up  and  cased  in, 
the  discharge  being  conducted  away  by  a  conduit  or 
box  long  enough  to  prevent  any  baffling  of  the  air,  and 
to  insure  the  taking  of  accurate  observations.  A  par- 
tition is  inserted  in  the  conduit,  at  a  distance  of,  say, 
fifty  feet  from  the  fan,  provided  with  a  movable  shutter 
by  which  the  discharge  or  flow  of  air  may  be  regulated 
from  the  outside ;  the  conduit  is  extended  beyond  this 
point  (having  a  uniform  sectional  area)  far  enough  to 
give  a  regular  and  established  velocity  to  the  discharged 
current,  the  object  being  to  provide  a  means  of  measur- 
ing the  current  of  air  produced  by  the  fan  :  the  object 


ECONOMIC   DISCUSSION   OF   THE   FAN.  8/ 

of  the  partition  or  regulator  is  to  establish  a  certain 
pressure  or  water-gauge  under  which  the  fan  will  work, 
and  which  will  represent  accurately  the  dynamic  pres- 
sure of  the  mine,  due  to  the  resistance  encountered  by 
the  current  in  its  passage  through  the  airways.  A 


Anemometer 


FIG.  VIII. 

water-gauge  is  inserted  in  the  side  of  the  conduit,  half 
way  between  the  fan  and  the  regulator,  as  shown  in 
Fig.  VIII,  and  an  anemometer  is  also  placed,  as  shown, 
some  distance  from  the  open  end  where  the  velocity  of 
the  current  will  be  uniform.  The  reading  of  the  ane- 
mometer may  be  taken  with  an  instrument  or  glass,  if 
convenient,  to  avoid  obstructing  the  free  discharge  of 
the  air.  The  fan  is  now  started  and  regulated  to  an 
exact  speed  of,  say,  50  revolutions  per  minute  ;  and  giv- 
ing a  few  moments  for  the  current  to  establish  itself, 
the  shutter  is  moved  in  the  regulator  until  a  certain 
fixed  water-gauge  is  obtained,  which  is  noted  :  as  is  also 
the  reading  of  the  anemometer,  from  which  the  quan- 
tity of  the  current  is  figured  ;  the  temperature  and 
height  of  barometer  being  likewise  noted  and  recorded. 
The  experiment  is  repeated  for  a  speed  of,  say,  75  revo- 
lutions per  minute,  and  like  observations  recorded  ;  and 


88  MINE-VENTILATION. 

again  for  a  speed  of  100  revolutions  per  minute.  Now 
by  substituting  these  recorded  results  and  the  known 
dimensions  of  the  fan  in  equation  (XXXVIII),  as 
previously  explained  in  this  chapter,  we  ascertain  the 
value  of  K  for  each  speed  of  the  fan  experimented 
upon ;  and  likewise,  by  substituting  in  equation 
(XLVII),  as  explained,  the  value  of  the  fan  constant 
for  this  type  of  fan  may  be  obtained.  The  fan  con- 
tant  is  the  same  for  any  particular  type  of  fan,  at  all 
speeds  of  such  fan.  The  subject  of  the  fan  as  a  motor 
is  one  of  the  most  important  subjects  relating  to  mine- 
ventilation,  and  should  be  carefully  considered  in  all  its 
bearings,  with  reference  to  details  of  construction,  by 
makers  as  well  as  by  all  others  who  are  in  any  way  con- 
nected with  the  operation  of  the  fan. 


SPLITTING   THE   AIR-CURRENT.  89 


CHAPTER  IX. 

SPLITTING  THE  AIR-CURRENT. 

Advantage  of  Splitting,  as  shown  by  Table  VI. — 

The  advantages  of  splitting  the  air-current  are  not  duly 
appreciated.  The  gain  from  this  source  is  so  enor- 
mous as  to  be,  in  many  cases,  disbelieved  by  practical 
miners  and  mine-operators  before  they  have  thoroughly 
investigated  the  subject.  In  order  to  make  apparent 
at  a  glance  the  effects  of  splitting  the  current  one  or 
more  times,  we  have  carefully  prepared  Table  VI, 
showing  the  respective  amounts  of  work  and  horse- 
power necessary  to  circulate  different  quantities  of  air 
through  different  mines,  and  also  through  the  same 
mine,  but  using  one,  two,  three,  etc.,  splits  successively. 
The  table  also  shows  the  unit  of  ventilating  pressure/, 
water-gauge  i  in  inches,  and  velocity  v  in  feet  per  min- 
ute at  which  the  current  travels. 

Mines  (assumed). — The  table  assumes  all  entries  or 
airways  to  be  6  X  8|-  feet,  giving  a  sectional  area  to 
each  individual  split  of  50  square  feet.  The  lengths  of 
the  several  air-currents,  including  the  returns,  are  as 
follows : 

Mine  No.  I.     Total  length  of  airway,     1,000  feet. 

"    «   2      (f      u    "     u      c  OOO   " 

"  ,  "  3.    "    "   "    "   10,000  " 

"   4.     "      "    "     "    20,000   " 

«     «    H       «       «     <(      u      TQ  ODD   '* 


90  MINE-VENTILATION. 

Mine  No.  6.     Total  length  of  airway,  40,000  feet. 
«     ^         «          «        <«         u        50,000     " 
"     8.         "          "       "         "       60,000     '• 

Quantity  Increased. — By  inspecting  the  table,  we 
see  that  with  the  same  power  we  can  increase  the  quan- 
tity of  air  any  given  number  of  times,  by  employing  a 
like  number  of  splits.  For  example,  it  requires  an 
application  of  70.690  horse-power  to  circulate  25,000 
cubic  feet  of  air  per  minute,  in  one  current,  through 
mine  No.  5  ;  but  by  splitting  into  two  currents  we  can 
circulate  50,000  cubic  feet  per  minute  in  that  mine 
with  the  same  power  ;  and  if  we  split  the  air  into  four 
currents  we  can  circulate  100,000  cubic  feet  per  min- 
ute by  the  application  of  the  same  power. 

Power  Decreased. — Again,  we  see  that  it  requires 
the  application  of  141.379  horse-power  to  circulate 
100,000  cubic  feet  of  air  per  minute  through  mine  No. 
8,  employing  four  splits  of  the  air-current ;  but  if  one 
more  split  is  made,  making  five  in  all,  the  power  nec- 
essary to  drive  the  same  air  is  only  a  little  more  than 
one  half,  viz.,  72.386  horse-power.  These  examples  serve 
to  illustrate  the  great  importance,  from  an  economic 
standpoint,  which  attaches  to  splitting  the  air  into  sev- 
eral distinct  currents,  to  say  nothing  of  the  avoidance 
of  danger  and  delay  in  case  of  local  accident,  when 
one  or  more  sections  of  the  mine  can  be  immediately 
and  completely  isolated. 

Limit  to  Splitting. — A  limit  to  the  indefinite  split- 
ting of  the  air-current  arises  from  the  consequent  re- 
duction of  the  velocity,  which  should  not  be  too  low, 
as  a  sluggish  current  will  not  remove  the  damps  or 
gases  which  hang  in  the  recesses  of  the  roof  and  sides, 


SPLITTING   THE   AIR-CURRENT.  9 1 

and  in  the  mouths  of  old  rooms,  etc.  Again,  a  high 
velocity  becomes  dangerous,  especially  in  fiery  mines, 
where  the  gases  may  become  ignited  by  the  flame  be- 
ing blown  through  or  against  the  gauze  of  the  lamp. 
The  limiting  velocities  of  the  current  may  vary  some 
under  varying  conditions,  but  practice  has  shown  that 
the  air  should  not  travel  less  than  four  nor  more  than 
twenty  feet  per  second.  At  the  working  face  a  veloc- 
ity of  five  or  six  feet  per  second  gives  go6d  results. 

Size  of  Airways. — There  should  be  a  regular  size  of 
airway  established  in  the  mine,  according  to  the  vol- 
ume of  air  we  expect  to  circulate,  that  the  velocity 
of  the  current  may  be  normal.  In  the  working  of 
low  coal  it  may  be  necessary  to  make  the  airways 
very  wide,  where  the  roof  is  not  taken  down,  in 
order  to  provide  a  sufficient  sectional  area.  As  stated 
in  the  foregoing  chapter,  the  air  should  be  brought 
down  the  shaft  and  through  an  airway  having  a  sec- 
tional area  double  that  of  the  main  airways,  as  far  as  to 
the  point  where  the  first  split  is  made. 

Arrangement  of  Splits.— As  far  as  possible,  all  the 
main  splits  should  be  made  as  near  as  practicable  to  the 
foot  of -the  downcast,  and  their  several  returns  join  the 
main  current  likewise  near  the  foot  of  the  upcast. 
This  will  reduce  the  resistance  of  the  pit  to  a  minimum 
by  reducing  the  distance  the  current  is  forced  to  travel 
at  a  high  velocity. 

Equal  Splits. — The  word  split,  as  used  in  reference 
to  mine-ventilation,  relates  to  the  division  of  the  air- 
current  :  as  used  in  this  book,  a  single  split  means  a  sin- 
gle undivided  current ;  two  splits  signifies  that  the  cur- 
rent is  divided,  and  is  travelling  in  two  separate  and 
distinct  currents  ;  equal  splits  refers  to  an  equal  divi- 


Q2  MINE-VENTILATION. 

sion  of  the  air  passing.  It  is  possible  without  the  use 
of  regulators  to  have  an  equal  division  of  the  air-cur- 
rent between  two  airways  which  differ  from  each  other 
in  every  respect. 

Unequal  Splits. — Where  the  division  of  the  air  be- 
tween two  airways  is  not  equal,  they  are  referred  to  as 
unequal  splits.  This  is  the  case  in  the  large  majority 
of  instances  where  the  ventilating  current  is  divided 
either  by  the  use  of  regulators  or  naturally. 

Natural  Division. — Now,  let  us  ask,  upon  what  prin- 
ciple or  in  obedience  to  what  law  does  the  division  of 
air  between  two  or  more  airways  take  place?  We  will 
state  here  in  answer  to  this  question,  what  will  be  ex- 
plained later  in  the  chapter,  that  the  division  of  the 
air-current  is,  in  obedience  to  the  law,  that  action  and 
reaction  are  always  equal.  Let  us  consider  for  a  mo- 
ment two  airways  open  alike  to  the  free  passage  of  the 
ventilating  current.  It  is  by  means  of  these  airways 
that  the  current  is  to  find  egress  from  the  mine  ;  behind 
it  is  the  power  of  the  motor  urging  it  forward  against 
the  resistance  of  the  airways :  it  is  the  resistance  that 
produces  and  maintains  the  ventilating  pressure ;  the 
power  behind  compels  this  pressure  to  move  at  a  cer- 
tain velocity  until,  exhausted,  it  reaches  its  limit,  and 
the  avp  of  the  airways  is  the  work  U  applied  to  the 
current.  Now,  between  the  works  being  performed  in 
these  two  airways,  counterbalanced  and  held  intact  by 
the  power  of  the  intake  current,  there  exists  a  dynamic 
equilibrium :  here  is  the  reaction  of  moving  forces  ;  the 
reaction  is  square  foot  against  square  foot  of  sectional 
area.  We  see  now  clearly  that  the  units  of  work,  or 
the  work  transmitted  by  one  square  foot  of  sectional 
area,  must  be  the  same  for  each  split.  The  expression 


SPLITTING   THE   AIR-CURRENT.  93 

for  this  unit  of  work,  in  terms  of  the  airways  and  their 
respective  currents,  is 


-      ......  <•> 


in  which  /  is  the  length  of  the  split,  o  the  perimeter  of 
the  airway,  etc.,  etc.     Hence  we  may  write 


from  which  we  may  write  the  proportion  applicable  to 
all  cases  of  splitting  where  the  division  is  natural  ;  that 
is  to  say,  where  no  regulators  are  used. 

G:0-:::      .....  (LIX) 


If  the  splits  in  question   have  the  same  cross-section, 
but  their  lengths  vary,  we  have 


Q  :  Q,  :  :      ,  :     L      ......     (LX) 

If  they  vary  in  their  length,  and  their  perimeters  are 
different  while  their  sectional  areas  are  the  same,  we 
have 

Q  :  Q,  :  :  VJ^:   VTo  ......     (LXI) 

Regulators.  —  Regulators  are  devices  by  which  the 
division  of  the  air  is  controlled  and  regulated  at  will. 
There  are  two  ways  or  methods  by  which  proportion- 
ate division  may  be  accomplished  ;  and  though  seem- 
ingly similar  to  the  casual  observer,  they  are  based 


94  MINE-VENTILATION. 

upon    essentially  different    principles  and   accomplish 
very  different  results. 

Present  Method. — The  method  in  general  use  at 
the  present  time  is  to  place  a  resistance  upon  the  re- 
turn of  those  splits  which  will  naturally  take  more  air 
than  the  desired  amount ;  the  resistance  thus  intro- 
duced being  created  by  means  of  an  obstruction,  as  a 
curtain  or  door  having  a  movable  shutter,  placed  in 
the  entry  so  as  to  retard  the  flow  of  the  air.  The  work 
of  the  box-regulator  is  discussed  and  shown  in  the  Ad- 
denda ;  but  we  will  say  here,  that  the  immediate  prac- 
tical effect  is  to  increase  the  ventilating  pressure  of  that 

split,  so  that  the  unit  of  work  ( — )  will  be  the  same  for 

all   the   splits   in   question.     We   readily  see   that  the 
unit  of  ventilating  pressure  in  any  split  will  be  inversely 


proportionate  to  [  _),  or  to  the  velocity  v  in  that  split, 
\a' 

and  that  by  enlarging  or  contracting  the  opening  in  the 
regulator  any  desired  proportionment  of  the  current 
may  be  secured.  From  what  we  have  shown  thus  far, 
it  is  readily  seen  that  in  this  method  of  splitting  by 
the  use  of  box-regulators  the  work  performed  in  each 
split  is  exactly  proportional  to  the  sectional  area  of 
that  split,  regardless  of  the  quantity  of  air  passing  in 
that  split  ;  for  the  reason  that  the  unit  of  work  at  the 
point  of  split  is  the  same  for  each,  and  the  full  area  of 
each  is  left  exposed  at  its  mouth,  and  each  split  conse- 
quently absorbs  an  amount  of  work  avp  proportionate 
to  its  area  a.  It  follows,  further,  that  the  work  per- 
formed in  that  split  in  which  there  is  no  regulator,  as 

indicated   by  the  expression  ( — ^-J  is  the   measure  of 


SPLITTING   THE   AIR-CURRENT.  Q5 

the  work  performed  in  each  split,  starting  from  the 
same  point  ;  and  the  total  work  of  these  splits  will  be 
found  by  multiplying  the  work  in  this  free  split  by  the 
number  of  splits. 

Objection.  —  The  objection  to  this  method  is  a  se- 
rious one  ;  viz.,  it  requires  the  introduction  of  a  large 
amount  of  foreign  resistance  into  the  airways,  and  the 
consequent  absorption  of  power,  for  which  the  operator 
receives  no  return.  This  absorption  of  power  is  large, 
as  will  be  shown  later. 

Another  Method.  —  Another  method,  and  one  which 
has  the  advantage  of  not  introducing  any  foreign  resist- 
ance into  the  airways,  is  to  divide  the  intake  air  ap- 
proaching the  mouths  of  two  or  more  splits  so  as  to 
apportion  the  applied  power,  the  avp  of  the  main  cur- 
rent, to  the  works  of  the  several  splits,  alvlpl  and  a^v^p^  , 
respectively.  This  is  accomplished  by  the  use  of  a 
form  of  regulator  to  be  described  later,  by  which  the 
exposed  area  Al  ,  A^  ,  etc.,  of  each  split,  respectively,  is 
made  proportional  to  the  above  respective  works  of 
those  splits,  according  to  the  proportion 


and  by  substitution  and  reduction  we  have 


From  this  proportion  the  exposed  areas  of  the  various 
splits  may  be  determined,  and  the  moving  forces pA^ 
=  p1al  and  pA9  =  pjtz  proportioned  to  their  respective 
works.  (See  Fig.  XI.) 


g  MINE-VENTILATION. 

Pro  and  Con. — It  has  been  said  by  some,  though 
not  with  much  apparent  forethought,  that  if  such  divi- 
sion of  the  air  were  to  be  made  at  the  mouth  of  the 
split  it  would  not  have  the  effect  to  change  the  moving 
force  pa  ;  arguing  that,  as  the  sectional  area  of  the  air- 
way again  enlarges  to  the  regular  size  immediately  be- 
hind the  point  of  split,  the  same  moving  force  would  be 
again  established:  forgetting  that  there  is  nothing  there 
to  re-establish  the  unit  of  ventilating  pressure/,  and  that 
in  the  expansion  of  sectional  area  immediately  behind 
the  point  of  split,  the  unit  of  pressure  has  fallen  from/ 
to  />, ,  which  latter  pressure,  pl ,  is  maintained  by  the  re- 
sistance inherent  in  this  particular  split.  We  stated  in 
the  introductory  chapter  that  the  dynamic  pressure 
which  animates  the  current  is  created  and  maintained 
by  the  resistance  ahead  of  the  current,  upon  which  it  is 
directly  dependent,  and  not  upon  the  power  behind  it. 
Were  it  not  for  this  resistance  there  would  be  no  pres- 
sure ;  we  would  have  an  illustration  of  the  third  case 
cited  under  "  Measure  of  Force,"  in  Chapter  II. 

Illustration. — This  can  be  proved  in  a  very  simple 
and  conclusive  way,  by  taking  a  short  tube  connected 
near  one  end  with  a  water-gauge,  as  shown  in  Fig.  IX, 
by  which  the  pressure  in  the  tube  will  be  indicated  any 


FIG.  IX. 


moment.     If  we  blow  into  the  end  marked  a,  the  other 
end  being  open,  there  will   be  no  appreciable  pressure 


SPLITTING  THE  AIR-CURRENT.  97 

indicated  by  the  water-gauge  ;  but  if  we  now  lengthen 
the  tube  by  the  successive  additions  of  lengths  of  tubing 
to  the  end  marked  b,  blowing  as  before  into  the  tube  at 
a,  we  will  observe  a  continual  rise  of  pressure  for  each 
additional  length :  such  pressure,  as  in  the  mine,  being 
created  and  maintained  by  the  resistance  offered  by  the 
tubing  to  the  flow  of  air. 

Conclusion. — It  is  then  a  most  important  point  to  be 
borne  in  mind,  viz.,  that  the  unit  of  ventilating  pressure 
/  is  created  and  maintained  directly  by  the  resistance 
ahead  of  the  current,  the  power  behind  the  current  giv- 
ing motion  or  velocity  ;  thus  these  terms  become  correla- 
tive, but  each  has  its  particular  source  or  derivative.  It 
is  as  the  spring  between  the  bumpers  of  a  railroad  train 
being  pushed  up  a  grade — the  steeper  the  grade,  the 
greater  the  resistance  and  the  consequent  pressure  upon 
the  spring :  the  power  of  the  engine  imparts  the  motion 
or  velocity  to  the  train  ;  but  it  is  perfectly  evident  that 
the  resistance  regulates  the  pressure  upon  the  spring: 
this  is  analogous  to  the  condition  which  exists  in  the 
mine  with  reference  to  the  ventilating  pressure.  Rea- 
soning further,  we  see  that  as  each  split  has  its  own 
particular  resistance,  it  should  have  its  own  unit  of  ven- 
tilating pressure,  denoted  by  /\,  />2 ,  etc.,  respectively. 
Each  split  will  have  its  own  particular  velocity,  denoted 
by  #, ,  v^ ,  etc.,  respectively,  dependent  upon  the  quantity 
of  air  required  and  the  sectional  area  of  the  split  or  air- 
way. Hence,  as  an  evident  consequence,  the  work  to 
be  accomplished  in  each  split  and  the  power  applied  at 
the  mouth  of  each  split,  and  consequently  the  exposed 
areas  At ,  A^ ,  etc.,  at  the  mouth  of  each  respective  split 
should  be  proportional  to  these  factors,  plvl,pjj^,  etc., 
respectively.  Let  us  now  summarize 


98  MINE-VENTILATION. 


THE  THEORY   OF  SPLITTING  AIR-CURRENTS. 

Dynamic  Equilibrium.— We  all  understand  what  is 
meant  when  we  speak  of  static  equilibrium  or  the  equi- 
librium of  pressures ;  but  we  may  not  so  clearly  com- 
prehend the  meaning  of  the  term  dynamic  equilibrium. 
When  a  force  is  exerted  to  produce  motion  against 
resistance,  as  alluded  to  in  Chapter  II,  there  is  devel- 
oped a  dynamic  or  moving  pressure,  which  in  connec- 
tion with  the  velocity  becomes  the  measure  of  the  force ; 
this  measure  (see  Chapter  IV)  we  call  work.  In  the 
illustration  previously  referred  to,  where  the  engine  is 
pushing  a  railroad  train,  the  dynamic  pressure  there 
developed  is  represented  by  the  compression  of  the 
spring  between  the  bumpers.  This  dynamic  pressure, 
as  we  have  seen,  is  a  factor  of  the  resistance  under 
which  the  moving  force  is  acting,  and  is  always  present 
as  an  active  agent;  in  no  way  promoting  or  retarding 
the  movement  of  the  body,  only  as  it  acts  as  a  medium 
between  the  resistance  and  such  portion  of  the  moving 
force  as  is  neutralized  by  that  resistance,  thereby  estab- 
lishing a  dynamic  equilibrium  between  these  two  com- 
ponents. This  affords  us  a  clear  comprehension  of  the 
forces  at  work  and  concerned  in  the  movement  of  a 
fluid  mass.  As  stated  above,  the  measure  of  the  ap- 
plied or  moving  force  is  this  dynamic  pressure  taken  in 
connection  with  the  velocity  of  the  movement ;  in  other 
words,  the  product  of  these  two  factors /z',  which  is,  as 
we  have  said,  the  work  of  the  force. 

Theory  of  Splitting.— Now  for  the  theory  of  split- 
ting;  and  by  this  we  mean  simply  the  action  of  the 
laws  concerned  in  the  splitting  or  dividing  of  currents 


SPLITTING   THE   AIR-CURRENT.  99 

of  air.  When  a  split  is  established  in  an  air-current,  and 
the  air  is  passing  in  proper  proportions  through  the 
respective  splits,  there  is  established  at  the  point  of 
split  a  dynamic  equilibrium  of  the  moving  forces;  in 
other  words,  these  forces  react  against  each  other.  Unit 
of  pressure  (pressure  upon  a  unit  of  surface)  reacts 
against  unit  of  pressure  ;  and  since  action  and  reaction 
are  always  equal,  the  units  of  work  (the  measure  of  such 
reaction)  will  be  equal.  Hence  we  may  write 

/»=/,».  .....  (Lxiii) 


Caution.  —  Equation  LXIII  is  always  true  at  the  point 
of  reaction;  but  we  must  not  mistake  the  units  of  work 
at  this  point  for  the  units  of  work  back  in  the  entry 
where  the  sectional  area  is  enlarged  to  the  regular  size. 
The  areas  at  both  of  these  points  are  transmitting  the 
same  work  obviously  :  it  could  not  be  otherwise.  Now 
if  the  work  to  be  performed  in  the  respective  splits  is 
different,  and  the  units  of  work  at  the  point  of  split  are 
equal,  our  problem  is  simply  to  proportion  the  exposed 
area  at  the  mouth  of  each  split  to  the  work  to  be  ac- 
complished in  that  split.  The  unit  of  work  as  here 
spoken  of  is  the  work  transmitted  by  one  square  foot  of 
sectional  area.  This  is  the  whole  theory  of  the  splitting 
of  air-currents. 

At  the  point  of  reaction  or  the  point  of  split  the  units 
of  work  (work  transmitted  by  one  square  foot  of  sectional 
area)  are  equal;  and  the  exposed  areas  at  the  mouths  of 
the  several  splits  must  be  proportioned  to  the  work  to  be 
performed  in  each  respective  split. 

Graphic  Method.  —  There  is  still  another  method  of 
demonstrating  this  important  law  ;  and  in  order  to 


100  MINE-VENTILATION. 

make  more  plain  the  action  of  the  law,  as  well  as  to  aid 
the  practical  mind  to  retain  the  points  gone  over,  we 
will  resort  now  to  an  every-day  illustration.  If  a  cer- 
tain blow  will  drive  a  certain  nail  one  inch  into  a  block 
of  oak,  the  same  blow  will  drive  the  same  nail  two 
inches  into  a  block  of  pine:  applying  this  principle  to  the 
movement  of  air  in  mines,  let  us  suppose  we  have  a 
current  of  100,000  cubic  feet  of  air  per  minute  coming 
down  the  intake  A,  animated  by  a  certain  unit  of  ven- 
tilating pressure/.  Arriving  at  a,  there  are  two  entries 
or  splits  open  to  its  passage  or  egress :  the  one,  B,  10,000 
feet  long;  the  other,  C,  5000  feet  long.  Each  of 
these  splits  has  its  respective  resistance  or  back  pressure, 
analogous  to  the  respective  densities  of  the  oak  and 
pine  blocks  referred  to  above.  Now  the  force  applied, 
corresponding  to  the  blow  upon  the  nail,  is  the  unit  of 
ventilating  pressure  multiplied  into  the  sectional  area 
of  the  entry,  or  pa,  the  moving  pressure.  This  force  is 
applied  alike  to  each  of  the  splits  B  and  C,  and,  follow- 
ing out  the  analogy,  will  drive  the  air  further  in  one 
minute  of  time  in  the  short  split  C  than  in  the  longer 
split  B.  In  other  words,  the  resulting  velocity,  and  con- 
sequently the  quantity,  will  be  greater  in  the  short  split 
than  in  the  longer  one ;  but  the  work  accomplished  in 
each  split  will  be  the  same,  because  the  same  moving 
force  pa  is  applied  to  each  split  under  the  same  condi- 
tions, and  must  perform  the  same  amount  of  work  in  the 
same  time.  The  hatched  portions  of  each  entry  (Fig. 
X)  represent  the  respective  quantities  or  velocities  in 
the  two  splits.  Now  in  performing  their  work  the  mov- 
ing forces  applied  to  the  splits  B  and  C  react  against 
each  other  and  against  the  moving  force  in  the  main 
entry  A  ;  this  is  evident.  The  reaction  is  unit  of  area 


SPLITTING   THE   AIR-CURRENT. 


101 


against  unit  of  area,  square  foot  against  square  foot ; 
hence  it  is  evident  that  the  units  of  work  or  the  work 
transmitted  by  a  unit  of  sectional  area  at  the  point  of 
split  will  be  the  same.  It  is  important  to  notice  that  the 
units  of  ventilating  pressure  may  be  unequal  although 
reacting  against  each  other,  the  rebound  from  such  re- 


FIG.  X. 

action  being  through  different  spaces,  or,  in  other  words, 
the  resulting  velocities  being  different.  The  unit  of 
ventilating  pressure  in  the  direction  of  either  split  can- 
not be  greater  than  the  resistance  of  that  split  will 
support;  as  we  have  previously  seen,  it  is  the  resistance 
ahead  of  the  current  in  each  split  that  maintains  the 
pressure  for  that  split. 

Style  of  Regulator  proposed. — The  style  of  regu- 
lator proposed  by  the  author  to  accomplish  the  propor- 
tionate division  of  the  intake  area,  and  give  to  the  mouth 
of  each  split  an  exposed  area  proportioned  to  the  work 
to  be  accomplished  in  that  split,  is  shown  in  Fig.  XI.  In 
this  figure  be  is  a  door  hinged  at  c  and  provided  with  a 
set-lock  at  bt  by  which  the  door  may  be  fixed  and  held 
firmly  in  any  desired  position.  The  current  of  air  com- 


102 


MINE-VENTILATION. 


ing  down  the  intake  A  strikes  the  edge  of  this  door  b  and 
divides.  It  is  evident  that  any  proportionate  division 
of  the  air  may  be  made,  as  the  door  may  be  set  so  as 


r— ,(  Work  \ 
\Pi\  1  a^vtpj 


FIG.  XL 

to  almost  entirely  shut  off  the  current  from  passing  into 
the  shorter  split,  by  which  it  seeks  to  find  egress  from 
the  mine,  and  cause  it  to  almost  wholly  pass  through 
the  longer  split. 

Argument. — The  question  has  frequently  been  asked 
by  intelligent  men,  "Wherein  does  this  form  of  regu- 
lator differ  from  the  one  already  in  use,  and  upon  what 
different  principle  is  its  action  based  ?  "  It  may  be  as- 
serted by  some,  after  a  cursory  investigation,  that  there 
can  be  no  essential  difference,  claiming  that  it  obstructs 
the  entry  in  the  same  manner  and  to  the  same  degree 
as  does  the  shutter-regulator.  Such  claims  are  based 
upon  no  fact.  The  difference  lies  in  the  fact  that  the 
splits  having  a  small  resisting  power  are,  by  the  use  of 
this  method,  ventilated  under  a  low  pressure,  and  not, 
as  in  the  other  method,  under  a  pressure  in  correspond- 
ence with  the  resistance  of  the  entire  pit.  This  results 
at  once  in  an  enormous  saving  of  power.  The  mouths 
of  the  several  splits  being  left  open,  in  the  one  method 


SPLITTING   THE   AIR-CURFENT.  IO3 

they  are  all  subjected  to  the  same  moving  force  pa ;  and, 
as  a  result,  in  those  splits  where  a  less  quantity  of  air  is 
desired,  or  where  the  resistance  is  small,  a  foreign  re- 
sistance must  necessarily  be  introduced  to  take  up 
and  neutralize  this  excess  of  power,  or  it  would  apply 
itself  to  the  movement  of  more  air  than  is  desired  in 
that  split.  In  other  words,  we  introduce  into  all  the 
lesser  splits  an  amount  of  dead  work  to  absorb  the 
surplus  of  power  applied  to  each,  making  the  work  to  be 
performed  in  each  of  these  splits  equal  to  the  work  of 
the  greatest  split  in  the  pit.  In  the  use  of  the  other 
method  the  power  applied  to  each  split  is  proportionate 
to  the  work  of  the  split. 

Illustration. — Let  us  now  assume  a  practical  case. 
We  will  suppose  mine  No.  8  to  be  passing  100,000 
cubic  feet  of  air  per  minute  in  four  splits,  as  follows: 

Split  a,    5,000  ft.  long. , 20,000  cu.  ft. 

"     b,  15,000  "     "     30,000"     " 

"     c,  20,000  "     "     30,000  "     " 

"      d,  20,000   "      "      20,000   "      " 


Total,  60,000  "     "     100,000  "     " 

If  there  were  no  regulators  used  in  any  of  these  four 
splits,  the  air  would  divide  itself  as  follows: 

Split  a 33,898  cu.  ft. 

"     b 23,390   "     " 

"      c 21,356    "     " 

"     d 21,356   "     " 

Now  it  is  evident  that  to  obtain  the  desired  quantities 
of  air  in  the  various  splits  some  artificial  means  must 


104  MINE-VENTILATION. 

be  resorted  to  that  will  decrease  the  flow  into  sections 
a  and  d,  and  cause  a  corresponding  increase  in  b  and  c. 
As  we  have  seen,  the  means  adopted  and  in  use  at  the 
present  time  is  to  place  an  obstruction — a  so-called 
"  Regulator  " — upon  the  return  of  those  splits  which 
naturally  take  more  air  than  the  desired  amount, 
thereby  driving  more  air  into  the  other  splits  which 
are  deficient.  We  have  had  this  method  under  discus- 
sion in  the  preceding  pages,  and  we  believe  it  has  been 
proven  to  result  in  a  profligate  waste  of  power ;  never- 
theless, to  make  this  more  plain,  we  have  tabulated 
below  a  comparison  of  the  horse-powers  consumed  in 
the  two  methods  alluded  to,  which  should  not  fail  to 
convince  any  who  still  remain  skeptical. 


Length. 

Nat.  Div., 

Req'd  Div., 

H.  Power, 

H.  Power, 

ft; 

cu.  ft. 

cu.  ft. 

Old  Way. 

New  Way. 

Split  a  . 

..   5,000 

33,898 

20,000 

81.439 

6.030 

"     b. 

..15,000 

23.390 

30,000 

81.439 

6l.O79 

11     c. 

.  .  20,000 

21,356 

30,000 

81.439 

81.439 

"    d. 

.  .  20,000 

21,356 

20,000 

81.439 

24.121 

Total. .  .60,000     100,000     100,000     325.756     172.669 

From  this  table  we  see  that  the  same  results  are  ob- 
tained in  both  cases  with  the  expenditure  of  but  little 
more  than  50$  of  the  power  in  the  new  method  than  is 
required  in  the  old. 

Objection.— It  has  been  further  objected  that  the 
placing  of  a  door  or  any  form  of  regulator  at  the 
points  indicated  would  block  the  main  roads  and  seri- 
ously interfere  with  the  working  of  the  mine.  But 
this  is  not  true  if  the  mine  is  properly  planned  and  a 
systematic  mode  of  ventilation  adopted,  as  will  readily 
be  seen  by  referring  to  Fig.  XII. 


SPLITTING  THE  AIR-CURRENT. 


105 


14,000 


Tail-Rope  Engine 

to  be  located  Jtere 

This  block  of  coal  to 
be  worked  out  later 


—  Door 
=.  Stopping 
X  Overcast 

^Regulator 


ft. 


IC>6  MINE-VENTILATION. 

System  in  Ventilation.— System  in  the  ventilation 
of  a  mine  is  everything.  One  of  the  first  points  to 
be  considered  is  the  disposition  of  the  main  haulage 
roads  with  respect  to  the  ventilating  currents.  A 
good  general  rule,  though  not  without  exception,  is  to 
make  the  return  air-courses  the  main  haulage  roads. 
This  plan  has  many  points  in  its  favor :  as,  the  avoid- 
ance of  doors  upon  the  haulage  roads  ;  the  freedom  of 
the  air-courses  from  the  dust  of  travel,  thereby  insur- 
ing a  pure  current  of  fresh  air  to  the  men  ;  the  main- 
taining of  a  warmer  temperature  in  the  hoisting  shaft 
in  the  winter  by  means  of  the  heat  of  the  upcast 
current,  thereby  preventing  the  formation  of  ice,  which 
otherwise  often  incapacitates  the  hoistways  ;  the  mov- 
ing of  the  loaded  cars  through  the  entries  in  the  same 
direction  with,  and  not  opposed  to,  the  circulating  cur- 
rent, thereby  offering  no  resistance  to  the  ventilation 
of  the  mine.  (The  resistance  to  the  ventilating  current 
arising  from  this  cause,  when  the  output  is  moving 
against  the  air,  is  often  very  considerable  and  almost 
as  often  overlooked  by  the  one  in  charge,  the  sluggish 
circulation  being  attributed  to  some  other  cause.) 
This  paragraph  may  seem  a  digression  from  the  sub- 
ject-matter of  the  chapter,  but  it  bears  directly  upon 
it,  inasmuch  as  it  refers  to  that  system  of  ventilation 
which  will  permit  of  the  arrangement  of  regulators  at 
the  mouths  of  the  several  splits  without  interfering 
with  the  working  of  the  mine. 

Effect  of  Dips  and  Rises. — There  is  one  more 
topic  that  demands  our  attention  before  leaving  this 
branch  of  the  subject.  It  is  the  effect  upon  the  circu- 
lating current  produced  by  a  rise  or  a  dip  in  the  air- 
way. We  have  seen  in  Chapter  III,  in  the  discussion 


SPLITTING  THE  AIR-CURRENT.  IO/ 

of  "  Dips  and  Rises,"  that  a  dip  or  a  rise  in  an  airway 
becomes  a  natural  factor  of  ventilation.  Its  effect 
upon  the  proportionate  splitting  of  the  air-current  is 
sometimes  misleading,  because  unlocked  for.  We 
often  hear  the  question  asked,  "Will  an  entry  going  to 
the  rise  or  to  the  dip  receive  its  proportion  of  air,  if 
from  any  cause  the  total  quantity  of  air  furnished  to 
the  pit  is  increased  or  decreased,  no  change  being 
made  in  the  regulator?"  We  answer,  undoubtedly 
the  proportion  will  change  for  every  change  in  the 
total  quantity  of  air  passing. 

Example. — To  illustrate :  Let  us  suppose  that  we 
have  100,000  cubic  feet  of  air  passing  into  our  pit  per 
minute;  and  we  have  divided  this  air  so  that  one  split 
running  level  is  receiving  50,000  cubic  feet  of  this  air, 
and  another  split  running  to  the  rise  is  likewise  receiv- 
ing the  same  amount.  If  now  a  fall  occurs  on  the  main 
air-course,  so  that  the  total  supply  of  air  to  the  mine 
is  thereby  reduced  from  100,000  cubic  feet  to  80,000 
cubic  feet  per  minute,  we  will  then  find  that  the  split 
running  to- the  rise  is  receiving  less  than  its  former  pro- 
portion of  the  entire  circulation  ;  i.e.,  less  than  40,000 
cubic  feet  of  air  per  minute.  If,  on  the  other  hand, 
the  circulation  of  the  pit  is  increased  to,  say,  120,000 
cubic  feet  of  air  per  minute,  this  split  running  to  the 
rise  will  receive  more  than  its  former  proportion  of  the 
air  ;  i.e.,  more  than  60,000  cubic  feet  per  minute.  In 
the  case  of  a  split  running  to  the  dip,  the  dip-split  will 
take  more  than  its  proper  proportion  when  the  circula- 
tion of  the  mine  is  decreased,  and  less  than  its  proper 
proportion  when  the  circulation  is  increased.  These 
results  may  be  tabulated  as  follows: 


108  MINE-VENTILATION. 

Rises.  Dips. 

Circulation  increased More.  Less. 

"          diminished..        ..Less.  More. 


Cause  for  Disproportion. — The  cause  for  such 
disproportionate  splitting  is  simple  and  obvious.  There 
exists  in  every  dip-split,  as  explained  in  Chapter  III, 
an  independent  factor  of  ventilation  or  a  ventilating 
power  which  is  generally  positive,  rarely  ever  negative. 
In  the  illustration  cited  above,  where  100,000  cubic 
feet  of  air  are  passing  per  minute,  this  ventilating 
power  in  the  dip-split  is  responsible  for,  say,  10,000 
cubic  feet  of  this  circulation  within  the  limits  of  the 
split;  i.e.,  this  factor  of  ventilation,  existing  in  this 
split  by  virtue  of  its  dip,  is  potent  to  draw  upon  the 
main  current  at  the  point  of  split  for  10,000  cubic  feet 
of  air  per  minute,  and  to  circulate  this  amount  through 
the  split.  The  balance  of  the  circulation  in  the  split 
and  throughout  the  pit  is  dependent  upon  the  ventilat- 
ing motor.  Now,  the  occurrence  of  a  fall  in  the  main 
entry  outside  of  the  split  in  question,  reducing  the  flow 
of  air  in  the  main  entry  at  the  split  to  80,000  cubic  feet 
of  air  per  minute,  does  not  affect  the  potency  of  the 
ventilating  power  existing  in  the  split ;  and  the  split 
still  continues  to  draw  from  the  main  current,  inde- 
pendent of  the  motor,  the  10,000  cubic  feet  per  minute, 
which  is  the  capacity  of  its  own  inherent  power.  This 
draught  upon  the  main  current  will  continue  as  long 
as  there  is  sufficient  air  passing  in  the  entry  to  supply 
the  demand  ;  and  we  further  venture  the  assertion  that 
should  the  fall  so  choke  the  main  entry  as  to  reduce 
the  total  supply  of  air  to  10,000  cubic  feet  per  minute, 
all  of  this  air,  upon  reaching  the  point  of  split,  would 


SPLITTING   THE  AIR-CURRENT.  109 

pass  down  the  dip-split,  and  none  would  find  its  way 
into  the  other  airway. 

Effect  Tabulated. — Now,  to  make  plain  the  fore- 
going, we  may  tabulate  the  effect  of  this  independent 
factor  of  ventilation  existing  in  the  dip-split  upon  the 
proportionate  division  of  the  air-current  as  follows: 

Before  the  fall : 

Main  airway 100,000  cu.  ft.  per  min. 

Level  or  rising  split,  50$. .    50,000   "    "    due  to  motor. 

Dip-split,  50^ J40'000   "   "      "     "  motor- 

(  10,000   "   "      "     "  dip. 

After  the  fall : 

Main  airway 80,000  cu.  ft.  per  min. 

Level  or  rising  split,  48.6$,  38,889    "    "    due  to  motor. 

Dip-split,  51.4*.  .  J  31, in    "    "      "     "   motor. 

(  10,000   "   "      "    "  dip. 

Thus,  by  a  reduction  of  2ofo  in  the  total  quantity  of  air 
passing,  the  dip-split  in  this  mine  takes  somewhat  more 
than  1000  cubic  feet  per  minute  beyond  its  propor- 
tion at  the  expense  of  the  other  split.  Analogous 
reasoning  will  show  the  effect  of  increasing  the  circula- 
tion, and  apply  likewise  to  rise-splits.  The  above  is 
figured  directly  from  the  principle  of  equation  (LIX). 


no 


MINE-VENTILATION. 


CHAPTER  X. 

DISCUSSION   OF   THE   "EQUIVALENT   ORIFICE." 

Prefatory. — Since  the  application  of  the  method  of 
the  "  Equivalent  Orifice  "  to  the  solution  of  problems  re- 
lating tofans  is  coming  somewhat  into  use, a  discussion  of 
its  merits  or  demerits  will  be  of  value,  and  perhaps  save 
us  from  error.  The  author  of  this  method,  M.  Mnrgue, 
deserves  credit  for  his  mathematical  deductions ;  but 
after  all  the  whole  method  is,  as  its  author  himself  says, 
simply  a  "  fiction."  It  is  a  generalization,  wherein  the 
passing  of  a  certain  current  of  air  through  a  mine  is 
compared  to  the  passing  of  the  same  current  through 
an  aperture  in  a  thin  plate. 

Illustration.  — To  simplify  this  and  make  it  plain  to 


FIG.  XIII. 


the  mind's  eye,  let  us  suppose  we  have  a  tank  of  water, 
as  shown  in  the  accompanying  figure.    One  of  the  sides 


DISCUSSION   OF   THE   "EQUIVALENT   ORIFICE."    Ill 

of  this  tank  is  pierced  near  the  bottom  with  a  round 
hole.  The  tank  is  made  of  thin  boiler-plate.  A  con- 
stant stream  of  water  flowing  into  the  tank  above, 
maintains  the  level  of  the  water  in  the  tank  at  a  given 
height  k  above  the  orifice.  As  a  result  the  water  issues 
from  the  orifice  at  a  constant  velocity  z/,  determined  by 
the  equation  for  falling  bodies, 


.......     (i) 

from  which  we  have 


(2) 


Now,  knowing  the  area  of  the  orifice  a  and  the  velocity 
of  the  fluid  as  it  issues  v,  the  quantity  of  the  flow  Q 
will  be  expressed  by  the  equation 


or 

Q  =  aV^A  .......     (3) 

But  the  water  in  the  tank  is  pressing  from  all  directions 
toward  the  orifice,  giving  rise  to  a  baffling  arid  a  con- 
sequent loss  of  velocity  at  the  orifice,  which  is  only  re- 
stored by  a  contraction  of  the  area  the  flow  just  beyond 
the  orifice.  This  contraction  of  area,  called  in  Physics 
the  "  Vena  contracta,"  is  dependent  for  its  amount  upon 
the  style  of  the  orifice  ;  but,  for  a  round  hole  in  a  thin 
plate  it  has  been  determined  as  0.65  of  the  original 
area  a.  Hence  we  have 

<2  =  0.65*  1/2^:      ....     (4) 

Now  as  the  laws  governing  the  flow  of  all  fluids  under 
like  conditions  are  the  same,  and  as  air  is  a  fluid,  it  is 


112  MINE-VENTILATION. 

suggested  by  Murgue  to  assimilate  our  formulas  expres- 
sive of  the  flow  of  air  through  mines  to  the  above, 
letting  Q  represent  the  quantity  of  air  passing  in  cubic 
feet  per  second,  h  the  head-of-air  column  in  feet,  and  a 
the  equivalent  orifice  of  the  mine.  Reducing  this  to 
cubic  feet  per  minute  and  inches  of  water-gauge  i,  we 
have  finally  for  the  value  of  the  equivalent  orifice, 

a  =  0.000383^.     .     .     .     (LXIV) 

Equation  (LXIV)  gives  the  value  of  the  area  of  the 
imaginary  equivalent  orifice  a  in  terms  of  the  quantity 
of  air  passing,  and  the  pressure  which  animates  such  cur- 
rent. This  is  true  enough,  and  so  far  the  analogy  drawn 
is  correct,  the  flow  of  a  fluid  through  an  aperture  in 
a  thin  plate  being  correspondent  to  the  flow  of  air 
through  a  mine.  Murgue  then  proceeds  to  show  the 
practical  utility  of  this  imaginary  orifice  by  supposing 
a  fan  to  be  revolving  at  a  uniform  speed,  discharging 
its  air  through  two  orifices  in  thin  plates  successively  : 
one  of  these  orifices  he  uses  to  represent  the  fan  and 
the  other  to  represent  the  mine.  Now,  as  he  says,  he 
has  in  effect  replaced  the  resistance  offered  by  the  fan 
to  the  passage  of  the  air  through  itself,  by  the  first 
plate,  and  the  resistance  of  the  mine  by  the  second 
plate.  From  this  point,  however,  Murgue  fails  in  the 
application,  because  he  assumes  that  the  effective  de- 
pression is  equal  to  the  initial  depression  minus  the 
depression  caused  by  the  passage  of  the  air  through  the 
fan.  Let  us  look  carefully  at  this  matter  of  depressions 
and  first  form  a  clear  idea  of  the  significance  of  the  term. 
It  relates  primarily  to  the  depression  of  the  water  in  one 


DISCUSSION   OF  THE   "EQUIVALENT   ORIFICE."    113 

arm  of  the  water-gauge.  It  is  synonymous  with  "  Unit 
of  pressure."  Murgue's  assumption,  then,  makes  the 
unit  of  pressure  due  to  the  resistance  of  the  mine  plus 
the  unit  of  pressure  due  to  the  passage  through  the  fan, 
equal  to  the  initial  unit  of  pressure.  This  is  undoubt- 
edly true  of  the  respective  works  of  these  pressures,  but 
is  not  true  of  the  pressure  themselves,  as  was  stated  in 
the  introductory  chapter.  No  one  will  deny  for  an  in- 
stant that  the  work  lost  in  the  passage  of  the  fan  plus 
the  work  performed  by  the  current  in  the  mine  repre- 
sents the  total  work  of  the  fan,  or  the  initial  work ;  but 
if  the  sum  of  the  two  works  is  the  initial  work,  the  sum 
of  the  two  pressures  cannot  give  the  initial  pressure, 
except  and  only  when  the  velocities  with  which  these 
pressures  move  are  equal.  In  the  consideration  of  falling 
bodies,  the  height  through  which  the  body  falls  is  gen- 
erative of  the  velocity.  The  method  of  the  Equivalent 
Orifice  treats  of  pressure  in  the  same  manner  as  genera- 
tive of,  or  at  least  correspondent  to, the  established  veloc- 
ity. This  can  only  be  true  for  the  same  equivalent  orifice; 
when  the  equivalent  orifice  remains  unchanged,  the 
same  pressure  will  always  indicate  the  same  velocity. 
Therefore  the  fallacy  of  this  ingenious  method  lies  in 
adding  together  the  pressure  due  to  the  passage  of  the 
air  through  the  equivalent  orifice  of  the  fan  (called  by 
its  author  the  "  Orifice  of  passage")  and  the  pressure 
due  to  the  passage  of  the  same  current  through  the 
equivalent  orifice  of  the  mine,  and  calling  their  sum  the 
initial  pressure  of  the  fan. 

It  is  important  to  remember  that,  while  in  statics  we 
equate  pressures,  in  dynamics  work  must  always  form 
the  basis  of  comparison. 

Further,  we  should  always  study  to  avoid  vague  and 


1 14  MINE-VENTILATION. 

imaginative  reasonings  as  far  as  possible,  never  dealing 
in  fiction  where  the  case  will  admit  of  absolute  demon- 
stration. It  is  due  to  the  failure  to  reduce  his  compari- 
sons to  a  basis  of  work  that  Mr.  Murgue  finds  no 
expression  in  his  formulas  for  the  width  of  the  fan-blade, 
which  is  a  most  serious  omission  ;  as,  also,  the  tem- 
perature of  the  air  and  the  height  of  the  barometer 
should  appear  there.  These  are  all  factors  which 
increase  or  diminish  the  yield  of  a  fan  very  materially. 
What  the  author  has  said  in  this  chapter,  or  elsewhere 
in  the  book,  must  not  be  understood  in  the  light  of  criti- 
cism, but  rather  as  striving  to  interpret  more  truly 
Nature's  laws,  and  in  this  we  must  all  be  only  learners. 


COMPRESSIVE  VS.   EXHAUSTIVE  VENTILATION. 


CHAPTER  XL 

COMPRESSIVE  vs.   EXHAUSTIVE  VENTILATION. 

Prefatory. — The  subject  of  the  ventilation  of  mines 
would  not  be  complete  without  a  reference  to  the  rela- 
tive merits  of  these  two  systems.  Very  little  can  be 
said  that  has  not  been  already  said  in  regard  to  either 
of  them,  and  still  we  find  strong  advocates  of  each. 
As  a  rule,  however,  the  men  who  are  apparently  the 
strongest  advocates  of  either  systemcannot  giveany  ade- 
quate reason  for  their  preference  that  will  stand  the  test 
of  criticism.  The  fact  is  that  both  of  these  systems  are 
valuable,  and  alike  find  their  particular  adaptation  to  the 
varied  conditions  of  mine-ventilation.  The  one  or  the 
other  should  be  adopted  for  any  proposed  workings 
only  after  a  thorough  consideration  and  study  of  the 
conditions  to  be  encountered  in  such  workings;  and 
not  for  the  reason  given  by  one  mining  man,  much  to 
the  amusement  of  his  friends :  laying  a  rope  upon  the 
ground,  he  explained  his  preference  by  saying,  "You 
see,  gentlemen,  I  can  pull  that  rope,  but  I  cannot  push 
it." 

Plenum  System. — Compressive  ventilation  is  repre- 
sentative of  what  is  known  as  the  "  Plenum  "  system. 
It  is  ventilation  by  means  of  the  force-fan  or  some 
other  motor,  by  which  the  air  is  forced  into  the  mine 
and  through  the  airways  under  a  pressure  greater  than 
that  of  the  atmosphere. 

Vacuum   System. — Exhaustive    ventilation    is   the 


Il6  MINE-VENTILATION. 

representative  of  what  is  known  as  the  "  Vacuum  "  sys- 
tem. It  is  ventilation  by  means  of  the  exhaust-fan, 
furnace,  or  some  other  motor  by  which  the  pressure  in 
the  upcast  shaft  is  reduced  and  falls  below  that  of  the 
atmosphere. 

Difference. — The  essential  difference  between  these 
two  systems  lies  in  the  fact  that  the  one  is  a  high-pres- 
sure system  and  the  other  a  low-pressure  system.  The 
moving  or  ventilating  pressure  pa  is  the  same  in  both  ; 
at  least  there  is  no  appreciable  difference.  The  water- 
gauge,  showing  the  difference  between  the  pressures  of 
the  intake  and  the  return,  will  give  very  approximately 
the  same  reading  for  the  same  mine  under  like  con- 
ditions, when  the  air  is  forced  by  the  motor,  as  when  it 
is  exhausted.  The  same  volume  of  air  must  be  passing 
in  the  same  direction,  under  absolutely  the  same  con- 
ditions of  temperature,  barometer,  and  hygrometric 
state.  It  will  not  answer  to  observe  the  water-gauge 
when  the  fan  is  forcing,  and  then  to  reverse  its  action 
and  take  the  same  observation.  This  would  not  be  an 
adequate  test,  although  the  same  quantity  of  air  might 
be  passing  at  the  time  of  taking  the  two  observations : 
the  obstacles  met  with  and  the  resistance  to  be  over- 
come by  the  current  in  the  mine  would  not  necessarily 
be  the  same  ;  and  this  is  a  point  about  which  we  have  to 
be  assured  before  making  the  test.  In  the  one  system 
the  motor  acts  to  establish  a  pressure  in  the  mine  as 
much  above  the  atmospheric  pressure  as  it  is  below  it 
in  the  other  system. 

Comparative  Effects. — Now,  what  are  the  compara- 
tive effects  of  ventilating  by  these  two  systems  ?  The 
system  by  compression  establishes  an  actual  pressure 
in  the  pit  which  is  always  greater  than  the  atmospheric 


COMPRESSIVE   VS.   EXHAUSTIVE   VENTILATION.    117 

pressure,  inflating  the  pit  as  we  would  a  balloon.  As  a 
natural  result,  the  air  of  the  pit  seeks  vent  by  every 
fissure  or  crevice  open  to  its  egress.  This  may  seem  a 
trivial  circumstance  but  in  the  vicissitudes  of  mining 
it  has  often  proved  a  very  important  one.  The  fissures 
and  crevices  formed  in  the  roof  of  the  mine  by  the  gen- 
eral sinking  of  the  overlying  strata  often  extend  to  the 
surface,  frequently  opening  up  seams  from  which  ob- 
noxious and  dangerous  gases  issue.  If  the  air  of  the 
pit  is  under  compression  these  gases  will  be  driven  from 
the  pit,  in  place  of  being  drawn  into  it,  as  would  be  the 
case  were  the  ventilation  exhaustive.  This  finds  even 
more  practical  application  in  the  case  of  the  near  ap- 
proach to  old  workings,  in  which  dangerous  gases  are 
very  apt  to  have  accumulated.  Such  accumulations 
of  gases  find  easy  access  to  a  pit  under  exhaustion  ;  in 
fact,  without  warning  they  may  and  often  are  thrown 
out  upon  the  miner  in  great  volume.  The  writer  re- 
members at  one  time  tearing  out  a  brattice  shutting 
off  some  old  workings  where  there  had  been  an  exten- 
sive fire,  and  gas  had  in  all  probability  accumulated  in 
considerable  quantity  ;  when  the  first  small  opening  was 
made,  the  sound  was  like  the  rushing  of  a  mighty  wind, 
as  the  air  under  compression  in  the  pit  found  vent  into 
the  old  works,  where  the  air  was  dead.  There  was  no 
fear  of  this  possible  accumulation  of  gas  coming  out, 
although  for  the  time  some  of  the  miners  were  fright- 
ened. Giving  the  space  time  to  ventilate,  the  hole  was 
then  made  larger  and  the  workings  entered  with  im- 
punity. 

Again,  it  is  argued  in  favor  of  the  exhaustive  method 
of  ventilation,  that  accumulations  of  gases  in  old  rooms, 
in  crevices,  etc.,  do  not  increase  as  fast  as  when  they  are 


Il8  MINE-VENT  JLATION. 

driven  back  by  the  compression  of  the  air,  and  are  not 
as  great  a  menance  to  the  safety  of  the  pit.  The  claim 
is  that  these  gases  are  held  back  in  their  crevices  and 
corners  by  the  extra  pressure  of  the  compressive 
method  ;  and  if  at  any  time  this  pressure  is  relieved,  by 
the  stoppage  of  the  fan  or  by  a  fall  in  the  airway,  the 
pent  up  gases  will  then  issue  in  a  larger  volume  and 
prove  more  dangerous.  In  regard  to  this,  we  all  know 
that  the  pressure  under  which  a  pit  is  ventilated,  even 
in  the  compressive  method,  falls  far  short  of  the  pres- 
sure necessary  to  restrain  a  gas  from  expanding,  or  the 
pressure  arising  from  the  tension  of  such  gas.  Again, 
the  natural  tendency  of  a  body  of  gas  (by  the  law  of 
diffusion)  is  to  slowly  diffuse  itself  and  mingle  with  the 
surrounding  air,  and  this  tendency  is  as  great  under  the 
pressure  due  to  compressive  ventilation  as  it  is  under 
the  more  reduced  pressure  of  the  exhaustive  method. 
Were  the  gas  more  of  a  cohesive  body,  as  a  fog  or  other 
vapor,  this  argument  would  be  more  tenable.  It  is  true 
that  when  the  fan  stops  and  circulation  ceases  the  air- 
ways seem  to  be  at  once  filled  with  the  issuing  gases  ; 
but  the  gases  were  not  pent  up  by  the  pressure  due  to 
the  circulation,  nor  do  they  issue  now  in  any  greater 
volume  than  before  the  circulation  ceased.  They  are 
not  now,  however,  brushed  away  by  the  passing  current, 
but  accumulate  where  they  issue. 

An  argument  uncontrovertibly  in  favor  of  the  ex- 
haustive method  of  ventilation  arises  from  the  fact  that, 
in  the  short-sighted  economy  of  the  average  coal  opera- 
tor, the  fan  is  established  at  the  dump  or  in  close  prox- 
imity thereto;  and  it  not  infrequently  happens  that  the 
air  forced  down  the  shaft  to  furnish  the  breath  of  life  to 
the  hundred  or  so  men  compelled  to  breathe  it  is 


COMPRESSIVE   VS.    EXHAUSTIVE   VENTILATION.    I IQ 

partially  vitiated  before  it  starts  upon  its  journey, 
laden  as  it  is  with  the  odors  of  the  gob-pile  or  the  fur- 
nace-stack. In  this  respect  the  exhaust-fan  possesses  an 
unquestionable  advantage,  as  it  admits  of  the  downcast 
shaft  being  placed  entirely  away  from  the  other  outside 
works,  and  thereby  insures  a  supply  of  the  purest  air. 

Conclusion. — It  is  better,  in  order  to  provide  against 
possible  contingencies  that  may  at  any  time  arise,  to 
arrange  the  fan  so  that  it  may  be  converted  immediate- 
ly from  a  force-fan  into  an  exhaust,  or  the  reverse  of 
this.  This  is  usually  arranged  in  a  very  simple  manner 
by  constructing  an  air-tight  enclosure  in  such  a  way  as 
to  cover  the  eyes  of  the  fan  and  connect  them  with  the 


FIG.  XIV. 


top  of  the  shaft.  The  enclosure  should  have  a  sectional 
area  somewhat  greater  than  the  area  of  the  shaft,  and 
must  be  provided  with  a  pair  of  doors  upon  each  side  of 
the  fan  and  opposite  the  eyes,  as  shown  in  the  side-view 
and  marked  d,  d.  These  doors  may  have  a  half-circle 
cut  from  each  of  them,  if  necessary,  so  that  when  shut 
they  enclose  the  shaft  of  the  fan  ;  when  open  and  the 


120  MINE-VENTILATION. 

fan  is  forcing,  they  afford  unobstructed  access  of  the  air 
to  the  eyes  of  the  fan.  When  the  fan  is  forcing,  all  the 
doors  are  closed  except  the  ones  d,  d,  just  mentioned; 
these  are  thrown  wide  open  to  afford  free  access  for  the 
intake  air.  The  fan  is  then  working  in  its  normal  con- 
dition. When  it  is  desired  to  exhaust,  the  intake  doors 
d,  d  are  closed,  the  doors  in  the  side-casing  at  c  c  are 
swung  back  till  they  meet  in  the  centre  of  the  shaft, 
thereby  cutting  off  the  connection  of  the  mine  with  the 
circumference  of  the  fan  and  at  the  same  time  establish- 
ing its  connection  with  the  eyes  ;  an  opening  is  then 
made  in  the  face  casing  of  the  fan  by  throwing  back 
the  door  a  and  raising  slightly  the  door  b,  thus  giving 
free  exit  to  the  discharge  from  the  fan.  In  this  position 
of  the  doors  the  fan  is  an  exhaust-fan.  All  of  the  doors 
should  be  made  to  fit  as  tightly  in  the  casing  as  possible  ; 
they  may  be  provided  with  canvas  flaps  at  the  edges, 
if  necessary. 


CARE   OF   MINE,    AS   ASSISTING   VENTILATION,    121 


CHAPTER  XII. 

CARE  OF  MINE,  AS  ASSISTING  VENTILATION. 

Prefatory. —  Having  gone  over  the  ground,  as 
viewed  from  a  theoretical  standpoint,  let'us  now  look 
at  a  few  essential  practical  points  with  which  every 
mine  manager,  every  pit  foreman,  indeed  every  miner 
or  day-hand  employed  in  the  pit  should  be  familiar. 

Conduct  of  the  Air. — The  distribution  and  conduct 
of  the  air-current  through  the  pit  and  to  the  face  of 
the  workings  should  receive  the  constant  and  most 
careful  attention  of  the  pit  foreman,  approved  by  the 
mine  manager.  It  is  a  question  of  vital  importance, 
both  as  a  source  of  revenue  to  the  company  and 
health  and  safety  to  the  men.  The  carrying  of  a  large 
quantity  of  air  through  an  ordinary-sized  airway  for 
any  considerable  distance  should  only  be  tolerated 
when  there  is  no  alternative  ;  it  is  expensive,  as  the 
velocity  is  high  and  the  power  correspondingly  large  ;  it 
will  also  require  a  constant  watching  and  timbering  of 
the  air-course  to  prevent  a  fall  shutting  off  the  entire 
section.  When  possible,  the  system  of  ventilation 
should  be  such  as  to  distribute  the  air  from  the  foot  of 
the  downcast  evenly  over  the  entire  pit,  without  pro- 
ducing a  high  velocity  of  the  current  at  any  point,  and 
to  isolate  the  different  sections  of  the  mine,  giving  to 
each  its  own  independent  circulation.  The  velocity  of 
the  current  in  the  main  airways  of  the  several  splits 
should  preferably  not  exceed  10  or  12  feet  per  second  ; 


122  MINE-VENTILATION. 

though  this  velocity  may  be  increased  for  short  dis- 
tances to  20  feet  per  second.  We  find  it  sometimes 
higher  than  this,  but  always  at  a  large  expenditure  of 
power. 

Keep  Airways  Clean.— The  airways  leading  to  the 
workings  of  a  mine  should,  of  all  places  in  the  pit, 
be  kept  clean  and  pure.  Mules  should  not  be  allowed 
in  them  at  all ;  and  miners,  for  their  own  sake,  should 
abstain  from  any  nuisance  in  them.  This  should  be  an 
imperative  rule  of  every  pit,  and  its  enforcement  should 
be  insisted  upon. 

Air  Required  per  Minute  per  Man.— The  fixing  of 
the  amount  of  air  which  it  is  necessary  to  furnish  per 
minute  for  each  man  and  for  each  mule  is  in  many 
respects  wholly  arbitrary,  because  the  conditions  are 
different  in  almost  every  pit,  and  because  the  amount 
of  air  actually  vitiated  by  the  breathing  of  the  men  and 
animals  is  small  in  comparison  with  the  amount  ren- 
dered obnoxious  from  other  causes.  Nevertheless, 
experience  has  demonstrated  and  the  mining  laws  of 
most  states  and  countries  now  provide  for  the  mainte- 
nance of  a  definite  amount  of  air,  which  most  authori- 
ties agree  should  not  fall  short  of  100  cubic  feet  per 
minute  for  each  man  and  500  or  600  cubic  feet  per  minute 
for  each  mule.  But  even  this  law  must  be  modified  in 
mining  practice ;  as,  for  example,  in  the  working  of  a 
thick,  fiery  seam  of  coal  the  above  amounts  would  not 
be  sufficient  in  the  large  airways  to  carry  off  the  accu- 
mulating gases ;  while,  on  the  other  hand,  in  many 
thin  seams,  and  also  in  small,  non-fiery  mines,  the  above 
amounts  prove  much  too  large.  In  fiery  mines  espe- 
cially, the  velocity  of  the  air-current  is  an  essential 
factor,  and  hence  the  required  amount  of  air  should  be 


CARE   OF   MINE,   AS   ASSISTING   VETTILATIONTl  23 

taken  in  connection  with  the  size  of  the  airways  in  all 
such  cases,  to  insure  the  necessary  velocity. 

Room-stoppings. — Another  important  point  is  the 
stopping  up  of  old  or  abandoned  rooms.  This  should 
always  be  done  when  the  gob  has  a  tendency  to  fire ; 
as  is  the  case  when  the  coal  slack  has  been  mixed  with 
the  refuse.  If  the  stoppings  are  built  at  all  they  should 
be  well  built ;  for  their  object  is  to  prevent  the  air 
from  drawing  through  such  works  and  maintaining 
slow  combustion  in  them  ;  this  can  only  be  done  by 
making  such  stoppings  practically  air-tight.  A  poor 
stopping  is,  in  many  instances,  worse  than  no  stopping 
at  all. 

Entry-stoppings. — Entry-stoppings  are  even  more 
important  than  room-stoppings ;  because  upon  their 
perfect  construction  depends  the  circulation  of  the 
entire  pit ;  their  leaking  permits  a  constant  loss  of  air 
into  the  return,  so  that  the  full  amount  never  reaches 
the  face  of  the  workings  where  it  is  needed.  These 
stoppings  should  be  built  double  ;  i.e.,  two  walls  should 
be  built  a  foot  or  so  apart  and  the  space  between  them 
filled  with  sand  or  fine  dust  from  the  roads.  This  is 
work  which  should  not  be  slighted  ;  it  should  be  left  in 
the  hands  of  men  that  can  be  trusted. 

Break-throughs.  —  Small  or  contracted  break- 
throughs exert  an  untold  influence  upon  the  circulation 
of  a  mine.  The  area  of  any  break-through  between 
entries  should  not  be  less  than  the  area  of  either  of  the 
entries.  It  will  often  be  necessary  for  a  pit  boss  to  see 
that  his  orders  in  this  respect  are  carried  out,  and  com- 
pel entry-men  to  widen  all  narrow  openings.  It  is  a 
common  practice  in  most  mines  for  entry-men  to  store 
their  tools  in  the  last  break-through,  where  the  air- 


124  MINE-VENTILATION. 

current  is  passing  and  where  every  inch  of  area  should 
be  available,  instead  of  carrying  them  back  to  the  next 
break-through,  which  has  been  stopped,  but  still  affords 
ample  room  for  the  storage  of  tools.  This  practice 
should  be  prohibited,  as  it  is  an  imposition  upon  all  the 
men  located  upon  that  air,  and  an  absolute  loss  to  the 
company,  making  them  furnish  more  power  to  obtain 
the  same  amount  of  air. 

Double  Doors. — When  doors  are  in  use  upon  the 
main  roadway  and  the  roadway  at  any  point  taps  or 
opens  into  the  main  air-course,  such  point  should 
always  be  protected  by  the  use  of  double  doors  ;  i.e., 
two  doors  far  enough  apart  that  they  will  not  be  both 
open  at  the  same  time.  This  will  prevent  the  tempo- 
rary stoppage  of  the  circulation  of  the  pit,  and  is  very 
essential  in  many  instances. 

Overcasts. — Every  good  pit  foreman  will  put  in 
overcasts  on  the  main  roadways  wherever  the  develop- 
ment of  the  cross-entries  warrants  so  doing.  They  may 
seem  to  be  expensive,  but  this  initial  expense  is  more 
than  repaid  by  the  saving  in  current  expenses  for  trap- 
pers, to  say  nothing  of  the  avoidance  of  delays  to 
drivers,  if  trappers  are  not  employed.  The  overcast 
will  always  yield  a  more  steady  current  and  avoid  the 
annoyance  to  the  miners  of  having  their  air  cut  off  by 
some  careless  or  indifferent  man  setting  the  door  open 
and  leaving  it  so.  Did  mine  managers  realize  for  a 
moment  how  much  of  valuable  time  is  lost  to  the  com- 
pany from  this  source,  they  would  permit  nothing 
other  than  an  overcast  at  these  main  points.  Men 
cannot  and  do  not  work  when  their  supply  of  air  is  cut 
off. 

Undercasts. — In  some  rare  instances  we  find  under- 


CARE   OF   MINE,   AS  ASSISTING   VENTILATION.    12$ 

casts  preferred  to  overcasts ;  but  we  believe  that  expe- 
rience advocates  the  adoption  of  the  overcast.  The 
author  has  seen  the  airway  coming  from  an  undercast 
so  filled  with  fine  dust  as  to  be  decidedly  unpleasant 
and  hurtful  to  the  lungs ;  the  dust  arising  largely  from 
the  roadway  passing  over  the  framing,  making  it  practi- 
cally impossible  also  to  prevent  leaking  and  loss  of  air. 

Angles  in  Airways. — It  will  be  necessary  to  draw 
but  a  passing  attention  to  the  avoidance  of  all  sharp 
angles  in  airways  generally,  but  especially  in  the  main 
air-courses,  where  such  material  obstructions  add  largely 
to  the  resistance  of  the  pit. 

Stables. — The  arrangement  of  the  mine  stables  is  an 
important  point  with  respect  to  good  ventilation,  as 
too  often  they  are  located  upon  the  air-course  in  such 
a  manner  as  to  taint  the  air  passing  into  the  pit.  This 
is  not  good  judgment,  nor  is  it  good  policy  to  place 
the  stables  upon  the  return  of  the  air,  without  giving 
to  the  mules  a  fresh  supply  of  air.  The  mule  needs 
pure  air  and  plenty  of  it  for  his  wholesome,  as  well  as 
man  ;  treat  him  well,  if  you  expect  him  to  work  well. 
It  is  advisable  to  have  the  mule  stabled  as  near  to  his 


Hauling  Road 

Inside  Stable 

FIG.   XV. 


work  as  possible ;  it  is  also  advisable  to  have  his  stable 
located  at  no  great  distance  from  the  bottom  of  a  shaft, 
where  he  may  be  rescued  in  case  of  accident,  and 


126 


MINE-VENTILATION. 


by  means  of  which  his  fodder  may  be  sent  down  and 
the  refuse  of  the  stables  hoisted.  As  far  as  possible, 
let  these  requisites  be  taken  into  consideration  in  the 
location  of  the  stable;  but,  in  any  event,  let  the  egress 
from  the  stable  be  upon  the  return  of  the  air,  and  ven- 
tilate by  means  of  a  small  split  direct  'from  the  air. 
We  would  suggest  a  location  similar  to  that  in  the 
accompanying  figure.  The  entry-pillar  may  be  widened 
at  any  point  where  it  is  advisable  to  place  the  stable  ; 
or  it  may  be  located  on  the  other  side  of  the  entry,  as 
shown  in  Fig.  XVI.  In  this  latter  arrangement  the 


Air  Cours 


Air-TeaTc 


Hauling  Road 


Curtain 

Air-box, 
overcast 


FIG.  XVI. 


ventilation  of  the  stable  should  be  secured  by  means 
of  a  small  split,  carried  from  the  air-course  by  an  over- 
cast box.  By  this  means  the  mules  will  not  be  com- 
pelled to  breathe  the  outgoing  powder-smoke  and  gas 
from  the  workings ;  they  will  work  better  and  live 
longer.  On  no  account  should  the  stable  be  allowed 

£> 

upon  the  air-course.  The  main  stable  located  at  the 
shaft-bottom  maybe  arranged  as  shown  in  Fig.  XII. 


APPENDIX. 

TABLES  AND  PROBLEMS. 


128 


APPENDIX. 


TABLE   I. 

COMPARISON  OF  THE  FAHRENHEIT  AND  CENTIGRADE 
SCALES. 


Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

Fahr. 

Cent. 

-30 

—  34-4 

70 

21.  1 

1  80 

82.2 

280 

137-8 

—  20 

-28.8 

80 

26.6 

190 

87.8 

290 

143-3 

—  10 

-23-3 

90 

32.2 

200 

93-3 

300 

148.9 

0 

-17-7 

IOO 

37-7 

210 

98.9 

310 

154-4 

IO 

—  12.2 

no 

43-3 

212 

IOO.O 

320 

1  6o.O 

20 

-6.6 

120 

48.9 

2  2O 

104.4 

330 

165.5 

30 

—  i.i 

130 

54-4 

230 

IIO.O 

340 

I7I.I 

32 

o.o 

I4O 

60.0 

240 

115.5 

350 

176.7 

40 

4-4 

150 

65.5 

250 

121.  1 

360 

182.2 

50 

10.0 

160 

71.1 

260 

126.7 

60 

15-5 

170 

76.6 

27O 

132.2 

TABLES  AND   PROBLEMS. 


I29 


Pounds  of  Bit. 
Coal  burned 
per  hour 

- 

6o<?     t.-t. 

459  T  *3  14,000 

•d 

1 
§ 

7  +        7  + 

£ 

3 

v?     >O                             -v?     xn                                        m 

in 

C 

i 

1          1         7  + 

& 

^ 

-»!f    vn 

a 

°Q                     oq                      £* 

V 

oo                                o                               r-*» 

H 

°*                      o                      & 

odd 

Sp.  Heat  or 
Thermal  Units. 

. 

odd 

I 

w 
H/A 

|° 

* 

«?                     ? 

vr                             -^. 

1    ^                   i    ^                    O) 

ij       it       1- 

0    5                       ^   "                       #  + 

o                        5-                      «    - 

H                                                 0                                                 °       * 

Symbols. 

JZ                                                           O                                                            CT 

u                   ffi 

Constituents. 

C                                           U    52                                     W     jj 

a          '§  s.         §  o 
1          "S?         l> 

iz                tj  a*              <i 

130 


APPENDIX. 


TABLE    III. 

TENSION   OF   AQUEOUS   VAPOR, 

AT    VARIOUS    TEMPERATURES,   EXPRESSED    IN    INCHES    OF    BAROMETER. 


Deg. 
Fahr. 

Tension, 
inches. 

Pevg< 
Fahr. 

Tension, 
inches. 

Deg. 
Fahr. 

Tension, 
inches. 

Deg. 
Fahr. 

Tension, 

inches. 

-30 

0.010 

45 

0.316 

65 

0.616 

105 

2.18 

—  20 

0.016 

46 

0.328 

66 

0.635 

IIO 

2-53 

—  10 

O.O26 

47 

0-339 

67 

o  665 

H5 

2.92 

O 

O.O42 

48 

0-351 

68 

0.676 

120 

3-33 

10 

0.070 

49 

0.363 

69 

0.698 

125 

3-75 

20 

O.  IIO 

50 

0-375 

70 

0.721 

130 

4-34 

30 

o.  180 

5i 

0.388 

7i 

0.745 

135 

5-00 

32 

0.200 

52 

0.401 

72 

0.770 

140 

5-74 

33 

0.207 

53 

0.415 

73 

0.796 

145 

6-53 

34 

O.2I4 

54 

0.429 

74 

0.823 

150 

7.42 

35 

O.22I 

55 

0.443 

75 

0.851 

1  60 

9.46 

36 

0.229 

56 

0.458 

76 

0.880 

1/0 

12.13 

37 

0-237 

57 

0.474 

77 

0.910 

180 

I5-I5 

38 

0.245 

58 

0.490 

78 

0.940 

190 

19.00 

39 

0.254 

59 

0.507 

79 

0.971 

200 

23.64 

40 

0.263 

60 

0.524 

80 

I.OOO 

2IO 

28.84 

4i 

0.273 

61 

0.542 

85 

1.170 

212 

30.00 

42 

0.283 

62 

0.560 

90 

1.36 

43 

0.294 

63 

0.578 

95 

1.58 

44 

0.305 

64 

0.597 

100 

1.86 

TABLES   AND   PROBLEMS.  13! 


TABLE  IV. 

SPECIFIC    HEATS   OF   VARIOUS   GASES   AND   VAPORS, 

REFERRED  TO  WATER  AS  UNITY. 
Gas  or  Vapor.  Specific  Heat. 

Air ,..   0.2374 

Oxygen 0.2175 

Nitrogen 0.2438 

Hydrogen 3.4090 

Carbonic-oxide  gas 0.2450 

Carbonic-acid  gas 0.2163 

Ammonia  gas 0.5083 

Aqueous  vapor 0.4805 


TABLE   V. 

SPECIFIC  GRAVITIES  OF  VARIOUS  GASES  AND  VAPORS, 

REFERRED  TO  AIR  AS  UNITY. 
Gas  or  Vapor.  Specific  Gravity. 

Air i.oooo 

Oxygen 1.1057 

Nitrogen 0.9713 

Hydrogen 0.0693 

Carbonic-oxide  gas 0.9670 

Carbonic-acid  gas 1.5291 

Ammonia  gas 0.5367 

Marsh  gas o.  5 590 

Sulphuretted  hydrogen 1.1912 

Aqueous  vapor 0.6235 


132  APPENDIX. 

TABLE   VI. 

EFFECT   OF   SPLITTING   THE   AIR-CURRENT. 

NOTE. — Size  of  all  airways  is  6  X  8£  ;  making  the  perimeter 
feet,  and  the  area  of  each  individual  split  50  square  feet. 


& 

M 

P4    CO  ^t 

too 

I-OO    00 

M    M    co  ^f  too    t^OO 

0  O 

1-1    N 

CO  Tf  IOO 

1 

ffi 

inCO  O    CM 

cn  r»  10  M 

O    r^ 

g 

M  OO    CO 

O    M  CO    CO 

M     M 

CO  COO    M 

oo   co 

M 

M     M     Tt 

RM 

co  r^  o  t 

M     <3-  I^-   O 

0 

1^ 

M      " 

R^?2- 

•as 

-" 

o  -t 

M     -3- 

a 

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CO 
u~> 

M  -TOO 
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R  M 

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O  O  CO    O 

O  O  oo   O 

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M  CO 

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t^ 

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M   CO 

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M 

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M   O  r^  to 

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M    O 

CO    i-i 

co  o 
co  o 

co  t^  tr 

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r^  u~>  co  M 

en 

M    CO    O 

co  M  co  o 

M 

M 

M    M    CO 

M 

coco-* 

M  cocorr 

M     M 

M     W 

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r8 

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to 

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IO 

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^| 

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00 

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10    O      M 
tO    M     M 

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10    M    O      M 

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co  O  co  o 

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So 

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to  (^ 

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to  M    M 

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0 

to  M   O    M 

M     CO   T}-O 

M 

cn 

M     >-l     M 

rj-  voo 

M    C^^^t 

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M'M 

^?g 

IO   M 

Mine- 
potential. 

O 

o  -to  co 

O  O   to  to 

o  o  o  •<*• 

M      O 

to  co  co  to 

000   S 

rj-  r^ 

coco 

00 

COO  OO 

toco   r* 

00 
to  O 

coo   O   co  O 

00    -1- 

to 

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to 

M    M    IOCO    10 

co  M  r^  M 

in 

COO  CO 

rj-  10  toco 

M  O 

-1-  to 

Oco 

-too  M  r^ 

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to  O 
OCO 

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§ 

§§§ 

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S§§8 

0    0    O    0 

§ 

§§§ 

!§§§ 

88 

§8 

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88 

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" 

to  o   O 

M    M 

O    »o 
CO 

O    O    0    O 

O 

O    0    0 
^3-  too 

0   O   O   O 
co  -3-  too 

o  o 

CO  T 

0    0 
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TABLES  AND   PROBLEMS. 


133 


TABLE  VII. 


HORSE-POWER   OF   DIFFERENT   FANS   AT  VARIOUS 
SPEEDS. 

NOTE. — Dry  air;  temperature  60°  F.     Barometer,  30".    Efficiency, 
)%  at  50  revolutions  per  minute. 


Diam. 
ft. 

Inner 
Rad. 

Width  of 
Blade. 

Area  of 
Eyes. 

Horse-power. 

50  rev. 

ioo  rev. 

129.1  rev. 

10 

2'  6" 

2'0" 

30  sq.  ft. 

2.6o8 

27.814 

42.919 

2    6 

3-259 

34-768 

53.649 

3   o 

3-Qii 

41.721 

64.379 

3   6 

4-563 

48.675 

75-109 

4   o 

5-215 

55.629 

85.839 

12 

3   o 

2    6 

50  sq.  ft. 

6-759 

72.094 

111.247 

3   o 

8.  in 

86.513 

133.496 

3   6 

9.462 

100.932 

155.746 

4   o 

10.814 

US-SSI 

177.995 

14 

4  o 

3  o 

50  sq.  ft. 

14.461 

154.247 

238.014 

3   6 

16.871 

179-954 

277-683 

4  o 

19.281 

205.662 

317.353 

4   6 

21.691 

23L370 

357-023 

16 

4   6 

3   o 

125  sq.  ft. 

24.821 

264.758 

408.542 

3   6 

28.958 

308.885 

476.633 

4   o 

33-095 

353-on 

544.724 

4   6 

37.232 

397.138 

612.814 

5   o 

41.369 

441-263 

680.905 

18 

5   o 

3   6 

125  sq.  ft. 

46.594 

497.000 

766.907 

4  o 

53.250 

568.000 

876.466 

4   6 

59-906 

639.000 

986.250 

5   o 

66.562 

710.000 

1095.584 

20 

5    6 

4  o 

175  sq.  ft. 

81.438 

868.674 

1340.432 

5    o 

101.798 

1085.843 

1675.541 

6   o 

122.157 

1303.012 

2010.648 

134 


APPENDIX. 


TABLE 
CHANGE   IN  TEMPERATURE,    BAROM- 

SHOWING  THE   EFFECT   UPON  THE   YIELD    OF  A   FAN   RUNNING   AT 

NOTE. — The  conditions  are  assumed  to  be  such  as  to  yield  80,000 


o 

Temperature  (Fahr.). 

Hygrometric  State. 

jr 

-30 

—  20 

—  10 

0 

10 

70 

(cubic 

feet 

per  mi 

nute.) 

29" 

80902 

80284 

79684 

79101 

78534 

77984 

Dry. 

30" 

8l822 

81197 

80590 

80000 

79427 

78870 

3i" 

82721 

82089 

81476 

80879 

80300 

79737 

29' 

80900 

80281 

79679 

79093 

78521 

77965 

50^  Saturation. 

3o" 

8l820 

81194 

80585 

79993 

79415 

78852 

3i" 

82719 

82086 

81471 

80873 

80289 

79/20 

29" 

80899 

80279 

79675 

79086 

78509 

77946 

100$  Saturation. 

30" 

81819 

81192 

80581 

79986 

79404 

78834 

31" 

82718 

82083 

81467 

80867 

80279 

79/03 

TABLES  AND   PROBLEMS. 


135 


No.  VIII. 

ETER,  AND    HYGROMETRIC   STATE. 

A    CONSTANT    SPEED    AND    DISCHARGING    INTO 

cubic  feet  of  dry  air  at  a  temperature  of  o°  F. 


THE    SAME    MINE, 
and  a  barometer  of 


Temperature  (Fahr.) 

L 
Is 

30 

40 

5° 

60 

7° 

80 

90 

77449 
78329 
79190 

76928 
77803 
78658 

(cubic 
76421 
77290 
78139 

feet  per 
75927 
76790 
77634 

minute.) 
75445 
76303 
77142 

74976 
75828 
76661 

745i8 
75365 
76193 

29" 
30" 
31" 

77419 
78300 
79162 

76883 
7776o 
78617 

76358 
77230 
78081 

75840 
76706 

77552 

75328 
76189 
77031 

74816 
75672 
76509 

74303 

75155 
75987 

3o" 
31" 

77389 
78271 

79T34 

76839 
777i8 
78577 

76296 
77170 
78023 

75755 
76624 
77472 

75214 
76078 
76923 

74661 

75520 
76361 

74096 
74953 

75789 

29" 
30" 
31" 

136 


APPENDIX. 


TABLE    IX. 

CHANGE  IN  TEMPERATURE,  BAROMETER,  AND 
HYGROMETRIC  STATE. 

SHOWING   THE  EFFECT   UPON   THE    SPEED    OF  A   FAN. 

NOTE. — The  power  applied  remaining  the  same,  any  change  in 
atmospheric  conditions  will  produce  a  corresponding  change  in  the 
speed  of  the  fan,  and  the  quantity  of  air  produced  will  remain  practi- 
cally unchanged. 

The  following  table  is  figured  from  a  base  of  100  revolutions 
per  minute,  at  a  temperature  of  60°  F.  and  a  barometer  of  30",  the 
air  being  dry.  The  fan  is  a  12-foot  fan,  30"  wide,  giving  an  effi- 
ciency of  90$  at  a  speed  of  50  revolutions  per  minute,  being  the  same 
fan  as  the  12-foot  fan  mentioned  in  Table  X;  it  is  also  found  recorded 
in  Table  VII. 


Temperature, 
Fahr. 

Barometer, 
inches. 

Hygrometric 
State. 

Revolutions 
per  minute. 

Horse-power. 

-30° 

28 

Dry. 

95-7 

72.094 

30 
30 

Saturated. 

93-4 
93-4 

" 

60° 

28 

Dry. 

102.7 

« 

30 
30 

Saturated. 

100.  0 

100.3 

» 

31 

" 

99.0 

100° 

28 

Dry. 

105.8 

" 

3° 
30 

Saturated. 

102.9 
103.8 

" 

TABLES  AND  PROBLEMS. 


137 


TABLE    X. 

SPEED    AND    HORSE-POWER    OF  DIFFERENT    FANS    AT 
DIFFERENT  MINES. 

NOTE. — Mine  :  Size  of  all  airways,  6  X  8|-. 

Motor  :  12-ft.  fan,  30  in.  wide,  6-ft.eye;  "area  of  the  two  eyes, 

50  sq.   ft.  ;    efficiency,  90$  at  50  revs,  per  min.  ;    max. 

effect,    speed,    129.1  revs,   per   min.  ;    limit    of    power, 

111.247  h.p. 
Conditions  :  Temp.  60°  F.,  barom.,  30  in.,  air  dry. 


Mine 
No. 

Quantity, 
cu.  ft.  p.  m. 

No.  of 
Splits. 

Length, 

Ft. 

Mine- 
Potential. 

Revolu- 
tions p.  m. 

Horse- 
power. 

25,000 

I 

5,000 

342.532 

58.0 

11.782 

2 

2 

685.064 

33-7 

1-473 

50,000 

I 

" 

342.532 

112.  0 

94.253 

2 

685.064 

58.0 

11.782 

25,000 

I 

10,000 

271.867 

70.3 

23-563 

'  ' 

2 

" 

543-734 

4O.2 

2.945 

3 

5O,OOO 

I 

271.867 

188  ^0*7 

2 

" 

543-734 

70.3 

23-563 

25,OOO 

I 

20,000 

215-781 

86.5 

47.127 

'  ' 

2 

" 

43L563 

48.2 

5.891 

4 

5O,OOO 

I 

<  < 

211;.  781 

^77    old. 

2 

« 

43L563 

86.5 

47.127 

3 

647.344 

60.8 

13.963 

138 


APPENDIX. 


TABLE    X.   (Continued^ 

SPEED    AND    HORSE-POWER    OF    DIFFERENT    FANS    AT 
DIFFERENT  MINES. 

NOTE. — Mine  :  Same  as  before. 

Motor  :  i6-ft.  fan,  36  in.  wide,  g-ft.  eye;  area  of  the  two  eyes, 

125  sq.   ft.  ;  efficiency,  90$  at  50  revs,   per  min.  ;  max. 

effect,    speed,    129.1    revs,    per   min.  ;    limit   of  power, 

408. 54  h. p. 
Conditions  :  Same  as  before. 


Mine 
No. 

Quantity, 
cu.  ft.  p.  m. 

No.  of 
Splits. 

Length, 

Mine- 
Potential. 

Revolu- 
tions p.  m. 

Horse- 
power. 

5O,OOO 
IOO  OOO 

2 
3 

2 

3O,OOO 

377.004 
565.507 

377  004 

66.4 

47.8 

70.690 
20.945 

565    521 

5 

ft 

3 
4 

« 

565.507 
754.009 

85.6 
66.4 

167.562 
70.690 

150,000 

4 
6 

" 

754.009 
942.5H 
1131.013 

96.3 
77-7 
66.4 

238.575 
122.  152 
70.690 

75,000 

1C 

IOO  OOO 

2 

3 
4 

5 

2 

40,000 

342.532 
5I3.79S 
685.064 
856.330 

342.  532 

107.7 
72.0 

56.7 
47-5 

318.  ioo 

94-253 
39.762 
20-359 

754.O2I 

6 

4 
6 

" 

685.064 
1027.595 

72.0 
51.6 

94-253 
27.927 

150,000 

4 
6 

8 

t  < 

685.064 
1027.595 
1370.128  i 

107.7 
72.0 
56-7 

3I8.IOO 
94-253 

TABLES   AND   PROBLEMS. 


139 


TABLE   X.    (Concluded) 


SPEED    AND    HORSE-POWER    OF    DIFFERENT   FANS  AT 
DIFFERENT  MINES. 

NOTE. — Mine  :  Same  as  before. 

Motor  :  2o-ft.  fan,  48  in.  wide,  n-ft.  eye;  area  of  the  two  eyes, 
(net),   125  sq.  ft.  ;  efficiency,  90$  at  50  revs,  per  min.  ; 
max.  effect,  speed,  129.1  revs,  per  min.*;  limit  of  power, 
1340.432  h.p. 
Conditions  :  Same  as  before. 


Mine 

No. 

Quantity, 
cu.  ft.  p.  m. 

No.  of 
Splits. 

Length, 
Ft. 

Mine- 
Potential. 

Revolu- 
tions p.  m. 

Horse- 
power. 

IOO,OOO 

2 

4 
6 

50,000 
« 

317.978 
635.956 
953-934 

103.2 
55-2 
40.1 

942.530 
117.817 

34  -  909 

7 

I5O,OOO 

4 
6 

8 

« 
« 

635.956 
953-934 
1271.912 

77-6 
55-2 
43-9 

397.629 
117.817 
49.704 

2OO,OOO 

4 
6 

8 

<« 

635-956 
953-934 
1271.912 

103.2 
70.0 

55-2 

942.530 

279.268 
117.817 

IOO,OOO 
i  < 

2 

4 
6 

6o,OOO 

299.229 
598.458 
897.687 

in.  8 

58.0 
42.0 

1131  .029 

141.379 

41  .890 

8 

150,000 

4 
6 
8 

«« 

598.458 
897.687 
1196.916 

81.9 
58.0 
46.1 

477.152 
141.379 
59.644 

2OO,OOO 
« 

4 
6 
8 

« 

598.458 
897.687 
1196.916 

in.  8 
73-8 
58.0 

1131.029 
335-120 
I4L379 

OP  THE 


NOTES 

EXPLANATORY  OF   THE   TABLES. 

TABLES  I,  III,  IV  and  V  need  no  explanation.  Table  II  is 
fully  explained  in  Chapter  VII. 

Table  VI. — From  an  inspection  of  Table  VI  we  see  that  by 
the  application  of  the  same  power  the  quantity  of  air  in  cir- 
culation is  increased  in  the  same  proportion  as  we  multiply  the 
number  of  splits.  Thus,  compare  lines  5,  9,  11,  15  and  23; 
these  all  represent  Mine  No.  5,  referred  to  in  the  early  part  of 
Chapter  IX ;  but  employing  successively  one,  two,  three,  etc., 
splits.  (The  term  "one  split"  as  hereused,  refers  to  a  single 
undivided  current.)  We  observe  the  power  in  each  instance  is 
70.690  h.p.,  while  the  quantities  in  circulation  hold  the  same 
proportion  to  each  other  as  do  the  number  of  splits  employed. 

Again,  for  the  production  of  the  same  quantity  of  air  per  min- 
ute in  the  same  mine,  the  powers  required  are  inversely  pro- 
portionate to  the  cubes  of  the  number  of  splits  employed. 
Thus,  compare  lines  15  and  19,  or  lines  16  and  20,  etc.,  of  the 
same  table. 

By  further  inspection  of  the  table  we  see  that  the  application 
of  the  same  power  to  different  mines,  or  to  the  same  mine  em- 
ploying a  different  number  of  splits  (which  is  practically  a  dif- 
ferent mine,  as  far  as  the  circulation  is  concerned),  gives  a  dif- 
ferent water-gauge,  according  to  the  quantities  of  air  yielded 
in  each  respective  case.  Thus  in  the  table,  line  5  represents  a 
power  of  70.690  h.p.  applied  to  Mine  No.  5,  producing  a  single 
current  of  25,000  cubic  feet  of  air  per  minute,  moving  under  a 
water-gauge  of  17.94  inches :  in  this  case,  the  power  is  applied 
to  a  current  compelled  to  move  against  a  mine-potential  of 
188.502.  Referring  now  to  line  23,  we  find  that  by  dividing  the 
circulating  current  into  six  separate  splits,  thereby  increasing 
the  mine-potential  to  1131.013,  the  same  power  applied  will 
yield  a  current  of  1 50,000  cubic  feet  of  air  per  minute  and  a 

140 


NOTES   EXPLANATORY    OF  THE  TABLES.          14! 

water-gauge  of  only  2.99  inches.  Hence,  we  see  the  fallacy  of 
taking  the  yield  alone,  or  the  dynamic  pressure  (water-gauge) 
alone,  as  expressive  of  the  power  of  a  fan.  To  say  that  a  fan 
will  yield  a  certain  quantity  of  air  per  minute,  running  at  a  cer- 
tain fixed  speed,  is  not  significant;  nor  yet  to  say  that  it  will 
produce  a  certain  water-gauge,  running  at  such  speed.  We 
must  know  the  power  developed  by  the  fan  at  that  speed, 
which  can  only  be  expressed  by  the  union  of  both  these  fac- 
tors. The  power  of  a  fan,  or  the  work  it  is  capable  of  perform- 
ing, indicates  its  value  as  a  motor.  » 

Again,  we  see  from  the  table  that  the  same  power  applied 
will  produce,  under  the  same  atmospheric  conditions,  quanti- 
ties proportionate  to  the  respective  mine-potentials,  or,  the 
mine-potential  remaining  the  same,  the  quantities  will  be  pro- 
portionate to  the  cube  roots  of  the  respective  powers. 

Table  VII. — This  table  shows  the  horse-power  developed 
by  the  fan  running  at  three  different  speeds,  the  last  being  the 
maximum  effective  speed  ;  and  consequently  the  powers  given 
in  that  column  will  be  the  limit  of  power  of  such  fan.  In  all 
of  the  tables  relative  to  fans,  we  have  assumed  a  temperature  of 
60°  F.,  a  barometer  of  30  inches,  and  a  dry  state  of  the  atmos- 
phere ;  we  have  also  assumed  all  of  the  fans  to  show  an  efficiency 
of  90$  at  a  speed  of  50  revolutions  per  minute,  which  efficiency 
would  give  a  maximum  effective  speed  of  129.1  revolutions  per 
minute.  Any  one  particular  fan  may  have  a  greater  or  less 
efficiency  than  this;  and  as  a  consequence,  its  maximum  effect- 
ive speed  may  be  above  or  below  this,  as  the  case  may  be,  as 
also  its  limit  of  power. 

An  important  showing  of  Table  VII  is  the  effect  of  the 
change  of  the  width  of  the  fan-blade  upon  the  power  of  the 
fan — the  power  varying  in  the  same  proportion  as  the  width  of 
blade  varies.  But,  the  proportionment  of  the  fan  and  the 
adaptability  of  the  different  dimensions  of  the  same  to  work  of 
different  kinds  have  been  carefully  considered, under  the  proper 
heads,  in  Chapter  VIII  and  will  not  be  repeated  here. 

Table  VIII.— Table  VIII  is  the  counterpart  of  the  last  preced- 
ing table,  and  shows  what  would  be  the  effect  upon  the  quan- 
tity of  air  produced,  due  to  change  of  temperature,  barometer, 
or  hygrometric  state,  were  the  speed  of  the  fan  to  be  maintained 


142  APPENDIX. 

at  a  uniform  rate.  The  table  presupposes  that  the  power  ap- 
plied is  changed  in  such  a  manner  as  to  maintain  a  constant 
speed  of  the  fan ;  and  is  useful  for  showing  the  relative  yields 
of  a  fan  under  varying  atmospheric  conditions.  For  example, 
if  our  fan  is  yielding  a  current  of,  say,  80,000  cubic  feet  of  air  per 
minute,  at  a  temperature  of  o°  F.,  and  a  barometric  pressure  of 
30  inches,  the  air  being  dry,  the  same  speed  of  that  fan,  when 
the  temperature  has  risen  to  90°  F.  and  the  barometer  stands 
at  29  inches,  the  air  having  become  saturated  with  moisture, 
will  only  yield  a  current  of  74,096  cubic  feet  per  minute. 

It  will  be  seen  from  the  table  also  that  the  effect  of  satura- 
tion upon  the  yield  is  very  much  greater  at  the  higher  temper- 
atures than  at  the  lower,  amounting  at  90°  F.  to  0.55$  of  the 
entire  yield,  while  at  o°  F.,  h  is  but  0.02$. 

The  effect  of  a  change  of,  say,  ten  degrees  in  temperature,  on 
the  other  hand,  is  less  at  the  higher  temperatures  than  at  the 
lower,  being  only  0.61%  of  the  yield,  in  rising  from  80°  F.  to 
90°  F. ;  while  in  rising  from  o°  F.  to  10°  F.  the  effect  is  0.72$ 
of  the  yield.  This  effect  of  a  rise  in  temperature,  at  any  point 
of  the  scale,  is  the  same  whether  the  air  is  dry  or  saturated 
with  moisture. 

The  effect  of  a  rise  or  fall  of,  say,  one  inch  of  barometric 
height  upon  the  yield  of  a  fan  is  constant,  between  the  same 
points  of  the  barometric  scale,  for  all  temperatures  and  whether 
the  air  is  dry  or  saturated  with  moisture.  This  effect  is  1.082$ 
of  the  entire  yield  when  the  barometer  falls  from  31  to  30 
inches,  and  1.127$  when  the  fall  of  the  barometer  is  from  30  to 
29  inches.  The  percentage  increases  slightly  as  we  drop  in  the 
scale. 

We  see  from  these  two  last  tables  that  a  meteorological 
change  will  not  produce  any  appreciable  change  in  the  power 
necessary  to  circulate  a  given  quantity  of  air,  but  will  simply 
vary  the  speed  of  the  fan.  It  will  take  more  power  to  produce 
a  certain  speed  of  the  fan  in  a  heavy  atmosphere  than  in  a  light 
one.  The  lesser  speed  in  the  heavy  atmosphere  will  produce 
the  same  quantity  of  air  per  minute  and  will  perform  the  same 
work  that  a  greater  speed  will  accomplish  in  a  light  atmos- 
phere, so  that  we  conclude  that  a  heavy  atmosphere  is  a  bene- 
fit to  the  working  of  the  fan,  providing  it  is  not  murky  or 


NOTES    EXPLANATORY    OF   THE   TABLES.          143 

foggy,  so  as  to  largely  increase  the  resistance  of  passage.  On 
the  other  hand,  the  heavy  atmosphere  may,  as  we  have  previ- 
ously stated,  increase  to  some  extent  the  resistance  of  the  pit, 
and  is  a  very  decided  hindrance  to  the  working  of  the  furnace, 
as  the  absorption  of  heat  for  the  same  rise  of  temperature  is 
greatly  augmented. 

Table  IX. — The  effect  is  here  shown  of  a  change  in  tem- 
perature, barometric  pressure,  or  hygrometric  state  upon  the 
speed  of  a  fan  operated  by  the  same  cylinder  pressure  or  power 
applied.  Our  table  assumes  that  the  application  of  a  constant 
power  (72.094  h.p.)  maintains  a  uniform  speed  of  fan  (100  rev- 
olutions per  minute)  when  the  temperature  of  the  atmosphere 
is  60°  F.,  barometric  pressure  30  inches,  and  the  air  dry;  and 
shows  that  if  the  temperature  were  now  to  rise  to  100°  F.,  the 
barometer  at  the  same  time  falling  to  28  inches,  the  air  still  re- 
maining dry,  the  speed  of  the  fan,  under  the  same  cylinder 
pressure,  would  increase  to  105.8  revolutions  per  minute.  The 
saturation  of  the  atmosphere  likewise  increases  the  speed  of 
the  fan,  other  conditions  remaining  unchanged.  The  power 
applied  remaining  the  same,  the  table  shows  that  atmospheric 
changes  produce  a  corresponding  change  in  the  speed  of  the 
fan.  Atmospheric  changes  produce  a  greater  effect  upon  the 
yield  of  a  furnace  than  they  do  upon  the  yield  of  a  fan,  be- 
cause, in  the  former  case,  they  affect  directly  the  power  of  the 
furnace,  which  is  the  power  applied  to  the  current ;  in  the 
latter  case  they  do  not  affect  the  power  applied,  which  is  the 
cylinder  pressure  of  the  engine,  and  is  assumed  to  remain  un- 
changed. If  this  power  applied  to  the  current  remains  un- 
changed, the  quantity  passing  will  also  remain  unchanged, 
although  there  is  an  almost  inappreciable  change  in  the  resist- 
ance of  the  mine,  which  would  affect  to  a  small  extent  the  quan- 
tity of  air  passing.  This  effect  is  so  small,  however,  as  not  to 
be  represented  in  our  formulas. 

Table  X. — This  table  is  for  the  purpose  of  showing  the  com- 
parative work  of  three  different  fans,  with  respect  to  their 
adaptability  to  different  grades  of  work.  The  atmospheric 
conditions  are  assumed  to  be  the  same  as  those  used  in  former 
tables.  Where  the  fan  is  incapable  of  performing  the  work  of 
any  given  mine,  dashes  have  been  inserted.  We  do  not  mean 


144  APPENDIX. 

to  intimate  for  a  moment  that  any  one  of  the  fans  mentioned 
is  well  adapted  to  all  of  the  work  of  which  it  is  here  shown  to 
be  capable;  for  example,  the  12  ft.  fan  is  evidently  not  well 
adapted  to  circulate  a  current  of  50,000  cubic  feet  of  air  per 
minute  through  Mine  No.  2,  in  a  single  split;  although  it  is 
capable  of  doing  so,  if  required.  It  is  crowding  its  speed  a  lit- 
tle and  the  area  of  its  eyes  is  none  too  large.  The  size  of  fan 
more  suitable  for  this  work  would  be  42  inches  wide  and  have 
a  y-foot  eye,  the  outer  diameter  remaining  the  same.  It  is  very 
important  that  the  internal  capacity  of  a  fan  be  proportionate 
to  the  quantity  of  air  it  is  expected  to  pass,  in  order  that  its 
efficiency  may  be  high.  The  proportionment  of  the  fan  has 
been  thoroughly  discussed  in  Chapter  VIII,  and  a  careful 
study  of  Table  X  will  serve  to  illustrate  the  principles  there 
referred  to.  Too  much  attention  cannot  be  given  to  this  part 
of  the  subject.  A  fan  not  proportioned  to  its  work  is  like  a 
man  staggering  under  a  burden  that  is  too  heavy  for  him  ;  or 
like  a  youth  compelled  to  grapple  with  a  problem  that  is  be- 
yond him.  The  result  is  dissatisfaction,  if  not  complete  fail- 
ure; and  the  thumping  of  the  engine,  the  racking  of  the  frame, 
and  the  straining,  wearing,  and  breaking  of  various  parts  is  evi- 
dence of  the  want  of  adaptation  of  the  machine  to  the  work  it 
is  compelled  to  perform. 

It  is  worthy  of  note  that  the  same  number  of  revolutions  per 
minute  of  any  fan,  under  the  same  atmospheric  conditions,  will 
always  develop  the  same  power. 

Conclusion. — The  study  of  the  tables  should  prove  of  great 
benefit  to  the  practical  mind.  We  do  not  doubt  that  many 
will  be  skeptical  in  regard  to  some  of  the  results;  but,  as  these 
are  in  accordance  with  the  known  and  accepted  laws  of  the 
mechanics  of  fluids,  they  should  be  received  or  disproven. 
Many  are  the  difficulties  attending  the  thorough  investigation 
of  this  subject ;  and  many  are  the  slight  occurrences,  some- 
times known,  but  more  often  unknown  to  the  investigator, 
which  destroy,  or  at  least  impair,  the  results  of  the  most  care- 
ful observations:  a  door  stands  open  in  the  entry;  one  or 
more  break-throughs  are  so  contracted  as  not  to  allow  the  free 
passage  of  the  current ;  loaded  coal-cars  standing  in  the  entries  ; 
dips  and  rises  not  taken  into  account ;  the  temperature  of  the 


NOTES   EXPLANATORY    OF  THE  TABLES.          145 

upcast  not  observed;  failure  to  observe  and  record  the  temper- 
ature and  anemometer  readings  at  various  points  in  the  pit,  so 
as  to  obtain  the  true  resistance  to  the  circulating  current ;  leak- 
ing of  stoppings ;  escape  of  exhaust  steam  from  pumps  or  in- 
spirators into  the  upcast;  influence  of  steam-pipes  extending 
along  the  entry  ;  upcast  or  downcast  shafts  obstructed  by  stair- 
ways, coverings,  tight  cages,  etc.  These  and  many  other  affect- 
ing causes  must  render  us  cautious  in  our  judgment  and  criti- 
cism. Before  making  investigations,  we  should  always  follow 
the  current  around  the  entire  pit,  carefully -noting  any  condi- 
tions which  might  influence  the  flow.  We  may  often  simplify 
our  task,  by  setting  open  one  of  the  main  doors  and  thereby 
shortening  the  course  of  the  current.  In  all  investigations  cf 
this  class,  we  should  carefully  avoid  being  too  minute  and  thus 
obtaining  coefficients  which  are  applicable  only  to  surfaces  of 
exact  measurement.  Practically,  we  are  dealing  with  mines  in 
respect  to  ihe  general  extent  and  size  of  their  air-ways ;  an  it  is 
of  little  moment  to  us,  whether  or  not  we  know  the  precise  co- 
efficient of  friction  for  air  rubbing  against  one  square  foot  of 
the  sides  of  those  air-ways.  The  actual  resistance  offered  by 
the  air-ways  of  a  mine  to  the  circulating  current  consists 
mainly  of  mechanical  obstructions,  such  as  entry-timbers,  jut- 
tings  of  the  ribs,  sharp  bends  or  angles  in  the  air-courses,  etc., 
whereby  the  momentum  of  the  current  is  broken.  What  we 
need  and  should  strive  to  ascertain  is  such  a  coefficient  as  will 
express  this  resistance  for  the  entire  mine,  reduced  to  one 
square  foot  of  rubbing  surface  and  a  velocity  of  one  foot  per 
minute.  We  mention  this  in  closing,  because  some  experi- 
ments which  have  been  recently  made  confine  themselves  too 
closely  to  minute  details,  which  are  more  valuable  as  a  scientific 
experiment  than  applicable  to  the  solution  of  practical  mining 
problems. 


PRACTICAL   PROBLEMS. 


1.  Find  the  weight  of  one  cubic  foot  of  dry  air  at  a  tem- 
perature of  30°  F.  and  a  barometric  pressure  of  30  inches? 

Ans.  0.0926783  I 

<0g  IS*  - 

2.  What  will  be  the  weight  of  the  same  at  a  temperature  of 

60°  F.  and  a  barometric  pressure  of  28  inches?  x 

Ans.  0.0715  Ib. 

3.  What  will  be  the  weight  of  one  cubic  foot  of  air  saturated 
with  aqueous  vapor  at  a  temperature  of  60°  F.  and  a  baromet- 
ric pressure  of  28  inches? 

Ans.  0.070996  Ib. 

Solution. — When  air  is  saturated  with  any  vapor  whatever, 
that  vapor  supports  a  part  of  the  barometric  pressure  equal  to 
the  tension  of  the  vapor  at  the  existing  temperature;  for  ex- 
ample, in  the  case  mentioned  in  problem  3,  the  vapor  of  satu- 
ration supports  0.524  inch  of  the  28  inches  barometric  pressure, 
and  the  air  supports  the  remaining  27.476  inches  (Table  III). 

We  first  find  the  weight  of  one  cubic  foot  of  dry  air  at  the 
given  temperature  (60°  F.)  and  a  barometric  pressure  of  27.476 
inches,  which  gives  0.0701617  Ib. 

We  then  find  the  weight  of  one  cubic  foot  of  dry  air  at  the 
given  temperature  and  a  barometric  pressure  of  0.524  inch 
(the  pressure  borne  by  the  vapor),  and  multiply  this  result  by 
0.6235  (the  specific  gravity  of  the  vapor,  Table  V).  This  last 
product  will  be  the  weight  of  the  vapor  saturating  one  cubic 
foot  of  air,  which  we  find  to  be  0.0008343  Ib. 

Finally,  adding  this  weight  of  vapor  of  saturation  to  the 
weight  of  dry  air  found  above,  we  obtain  for  the  weight  of  one 

146 


PRACTICAL  PROBLEMS.  147 

cubic  foot  of  saturated  air  at  the  given  temperature  and  press- 
ure 0.070996  Ib. 

4.  What  will  be  the  weight  of  one  cubic  foot  of  vitiated  air, 
at  the  foot  of  the  upcast,  assuming  that  the  air  is  here  com- 
pletely saturated  with  moisture  ;  temperature  70°  F.,  barometer 
30  inches,  and  the  oxygen  of  the  air  wholly  converted  into  car- 
bonic acid  gas  (CO2)  ? 

Am.  0.080805  Ib. 

Solution. — This  is  the  worst  case  which  can  occur,  as  far  as 
the  gaseous  composition  of  the  current  is  concerned  ;  for  the 
presence  of  carbonic  oxide  gas,  or  of  fiery  gases  in  the  current, 
would  aid  ventilation ;  but  it  is  here  assumed  that  the  oxygen 
of  the  air  is  wholly  converted  into  carbonic  acid  gas. 

We  find  the  weight  of  nitrogen  and  carbonic  acid  gas  which 
one  cubic  foot  of  air  would  yield,  by  substituting  the  given 
numerical  values  for  their  respective  quantities  in  equations 
i-XLIV  and  3-XLIV  ;  remembering  that  these  gases  support 
only  29.279  inches  of  the  30  inches  barometric  pressure,  the 
vapor  of  saturation  supporting  the  remaining  0.721  inch.,  be- 
ing its  tension  at  70°  F.  (Table  III).  The  weight  of  the  vapor 
of  saturation  is  then  found,  by  substitution,  in  equation  5-XLIV. 

As  a  result,  we  obtain  the  following  : 

Nitrogen 0.0564824  Ib. 

Carbonic  acid  gas. .  0.0231964    " 
Aq.  vapor o.ooi  1262    " 


0.0808050  Ib. 

5.  Referring  again  to  problem  4,  and  assuming  that  the 
average  temperature  of  the  upcast  is  70°  F.,  while  that  of  the 
downcast  is  60°  F.,  and  the  depths  of  both  the  upcast  and  the 
downcast  shafts  are  each  200  feet,  what  amount  of  back  press- 
ure per  square  foot  of  sectional  area  will  be  entailed  upon  the 
fan,  due  to  such  vitiated  condition  of  the  upcast  ? 

Ans.  0.83958  Ib. 

Solution. — We  find  the  weight  of  dry  air  at  a  temperature  of 
60°  F.  and  a  barometric  pressure  of  30  inches  to  be  0.0766071 


148  APPENDIX. 

Ib.  Deducting  this  from  the  weight  found  in  problem  4,  we 
have  for  the  difference  of  pressure  due  to  one  foot  of  vertical 
height.  0.0041979.  Multiplying  this  by  200,  the  depth  of  shaft, 
we  obtain  0.83958  Ib.  as  the  back  pressure  per  square  foot,  or 
the  unit  of  back  pressure. 

NOTE. — This  is  an  item  which  is  frequently  overlooked  in  investigations,  and  it 
may  at  times  exert  a  powerful  influence  over  the  circulation. 

6.  Express  the  unit  of  pressure  found  in  the  last  problem, 
in  terms  of  head-of-air  column.     (See  equation    II.) 

Ans.  10.96  ft. 

7.  Express  the  same  in  inches  of  water-gauge.    (See  equation 
XXXVI.) 

Ans.  o.i  6  in. 

8.  What  will  be  the  reading  of  a  water-gauge  inserted  between 
the  intake  and  the  return  of  an  air-split  10,000  feet  long;  size 

y       of  air-way  (6x8^)  feet;  when  50,000 cubic  feet  of  air  are  passing 
per  minute,  in  this  split? 

Ans.  2.99  ins. 

9.  Find  the  horse-power  of  the  air-split  mentioned  in  the 
last  problem. 

Ans.  23.563  h.p. 

10.  What  quantity  of  air  is  passing  per  minute  through  an 
air-course  whose  size  is  (6xio)   feet,  when  the  velocity  of  the 
current  is  10  feet  per  second  ? 

Ans.  36,000  cu.  ft. 

11.  In  a  certain  mine,  100,000  cubic  feet  of  air  is  passing  per 
minute,  in  four  splits  or  currents,  as  follows  : 

"A"  split,  (6x8^)  looo  ft.  long,  1 5,000  cu.  ft. 

44  B "       "         "  8000  "       "       20,000    "    " 

44  C"      "        "  6000  "      "       35,000    "    " 

"  D "      *'        "  4000  "      "      30,000    "    " 


PRACTICAL  PROBLEMS.  149 

The   division    is  accomplished  by  the  use  of  box-regulators. 
What  is  the  horse-power  of  this  pit  ?  ' 

Am.   isV^Vh.p. 

NOTE.— The  box-regulators,  which  are  necessary  in  splits  "A,"  "  B,  '  and  "  D," 
make  the  work  performed  in  those  splits  equal  to  the  work  in  split  "  C."  This  is 
the  great  disadvantage  of  the  use  of  this  form  of  regulator.  In  the  use  of  the 
other  form  of  regulator,  each  split  has  its  own  separate  work,  peculiar  to  itself,  as 
given  in  the  following  problem. 

12.  What  would  be  the  horse-power  of  the  pit  mentioned  in 
the  last  problem,  if  the  division  of  the  air  were  accomplished  by 
the  use  of  the  improved  regulator  ? 

Am.  "  A  "  split    0.509  h.p. 
"B"     "        9.651     " 
"C"    "      38.794    " 
"D"    "     16.287    " 


Total...  65.241    " 

13.  What  quantity  of  air  per  minute  will  100  horse-power 
produce,  under  a  three-inch  water-gauge? 

Ans.  21,154  cu.  ft. 

14.  What  will  be  the  unit  of  ventilating  pressure,  developed 
by  a  furnace  capable  of  maintaining  an  average  temperature  of 
300°  F.,  in  an   upcast  shaft  500  feet  deep;  the    depth   of  the 
downcast  being  the  same  and  its  average  temperature  60°  F. ; 
barometer  30  inches  ;  ignoring  the  vitiated  condition  of  the  up- 
cast air  ? 

Ans.   12. 1 1  Ibs. 
K 

15.  If  we  have  10,000  cubic  feet  of  air  passing  down  the  in- 
take of  a  mine  per  minute,  having  a  temperature  of  60°  F. ;  and, 
if  we  introduce  a  water-gauge  communicating  between  the  first 
of  the  air  and  the  last  of  the  return,  which  gives  a  reading  of 
1.5  inches';  what  will  be  the  volume  of  air  passing  per  minute 
upon  the  return  at  the  point  of  observation,  the  temperature 
here  having  increased  to  70°  F.  and  the  barometric  pressure  at 
the  same  point  being  30  inches;  supposing  no  augmentation 
of  the  volume  of  the  current  by  gases  from  the  mine  ? 

Ans.  10,230  cu.  ft. 


150  APPENDIX. 

Solution. — The  weight  of  air  passing  per  minute  through  the 
mine  is  obviously  the  same  at  all  points  of  the  air-course, 
supposing  there  to  be  no  leaks  through  doors  or  stoppings;  it 
is  unquestionably  the  same  at  the  two  points  of  observation. 
Hence,  by  referring  to  equation  XLIII,  we  see  that  the  vol- 
umes passing  these  two  points  are  inversely  proportional  to 
the  pressures  and  proportional  to  the  expression  (459  +  /) ;  and 
we  may  write  the  proportion, 

B,  B 


459  +  *i      459  +  / 

But  Bi,  the  barometric  pressure  at  the  point  of  observation 
upon  the  first  of  the  air,  may  be  determined  by  reducing  the 
inches  of  water  gauge  to  inches  of  barometer  and  adding  this 
to  the  barometric  pressure  given  upon  the  return,  according  to 
the  equation. 


I3-596 

Substituting  given  numerical  values  for  their  respective  quan- 
tities in  equation  2  above,  and  reducing,  we  find, 

Bi  =  30.1103  inches. 

Finally,  substituting  numerical  values  for  their  respective  quan- 
tities in  equation  i  above  and  reducing,  we  obtain  for  Q  the 
answer  given  above,  10,230  cubic  feet. 

16.  Suppose  a  mine  having  two  shafts,  each  200  feet  deep, 
to  be  ventilated  by  a  furnace.    Assume  the  outside  temperature 
to  be  60°  F.,  barometer  30  inches,  average  temperature  of  the 
upcast  200°  F. ;  and  also  assume  the  worst  condition  of  the 
vitiated  air  possible,   as  in  problem  4,  the  oxygen  of  the  air 
having  been  wholly  converted  into  carbonic  acid  gas  ;  and  the 
return   air  being  saturated  at  a  temperature   of  70°  F.  ;  what 
unit  of  ventilating  pressure  will  result? 

Ans.  2.348  Ibs. 

17.  What  unit  of  ventilating  pressure  would  result  in  the 


PRACTICAL  PROBLEMS.  151 

above  case  if  the  return  current  was  comparatively  free  from 
carbonic  acid  gas,  the  other  conditions  remaining  the  same? 

Ans.  3.364  Ibs. 

l^~ 

18.  What  unit  of  ventilating  pressure  would  result  in  prob- 
lem 17,  were  we  to  ignore  the  fact  that  the  return  air  is  satu- 
rated with  moisture  just  before  entering  the  influence  of  tlie 
furnace  ;  i.e.,  were  we  to  figure  this  problem  by  the  method  in 
general  use  in  our  text-books  ? 

Ans.  3.255  Ibs. 

NOTE. — Air  saturated  with  moisture  is  always  lighter,  bulk  for  bulk,  than  dry 
air  under  the  same  conditions. 

19.  In  a  certain  mine  ventilated  by  a  furnace,  10,000  cubic  feet 
of  air  are  passing  per  minute,  the  upcast  shaft  being  100  feet 
deep  ;  to  what  extent  would  this  circulation  be  increased  by 
building  a  chimney  over  the  shaft    16  feet   high,  other  con- 
ditions remaining  the  same  ? 

Ans.   10,770  cu.  ft. 

LS 

20.  What  quantity  of  air  would  pass  per  minute,  under  the 

unit  of  ventilating  pressure  (3.364  pounds)  found  in  problem 
17,  supposing  the  total  length  of  airway  to  be  10,000  feet,  the 
sectional  area  of  the  same  50  square  feet,  and  the  perimeter  28$ 
feet,  the  air  travelling  in  one  undivided  current,  using  Atkin- 
son's coefficient  and  ignoring  the  resistance  of  the  shaft? 

Ans.  8,222  cu.  ft. 

21.  What  quantity  of  air  would  pass  per  minute  in  the  last 
problem  were  we  to  split  the  current  once,  the  other  conditions 
remaining  the  same  ? 

Ans.  23,255  cu.  ft. 

22.  What  will  be  the  mine-potential  in  the  two  cases  respec- 
tively ? 

Ans.  ist  case,  271.868;  2d  case,  543.736. 

23.  What  horse-power  is  expended  in   these  two  cases  re- 
spectively ? 

Ans.  ist  case,  0.838  h.p. ;  2d  case,  2.371  h.p. 


152  APPENDIX. 

NOTE. — In  problems  14  and  16  we  assume  that  the  power  applied  is  changed  so 
as  to  maintain  the  same  unit  of  pressure  in  the  airways  after  the  current  is  split; 
we  have  in  these  two  cases  a  different  power  and  a  different  quantity  of  air  pass- 
ing per  minute. 

24.  If  we  have  100,000  cubic  feet  of  air  passing  per  minute  by 
the  expenditure  of  70.69  horse-power,  the  air  travelling  in  a 
single  current,  what  quantity  of  air  per  minuie  would  the  same 
power  yield  were  this  current  to   be  divided  into  two  equal 
splits? 

Ans.  200,000  cu.  ft. 

V 

25.  In  the  last  problem,  what  power  would  be  required  to  cir- 
culate the   100,000  cubic  feet  of  air  per  minute  in  two  equal 
currents? 

e     ^  -/  0rU*-*X?*'t3     ~  ->  Ans.  8.836  h. p. 


).  What  water-gauge  will  be  developed  in  the  case  just 
cited,  where  100,000  cubic  feet  of  air  are  passing  per  minute,  at 
an  expenditure  of  70.69  horse-power. 

Ans.  4.48  ins. 

27.  What  is  the  unit  of  ventilating  pressure  indicated  by  this 
water-gauge  ?  Ans.  23.33  lbs- 
y  2-*?,  JO 

28.  The  entire  length  of  airways  being  30,000  feet,  and  the 
sectional  dimensions  6  x  8|-  feet,  what  is  the  mine-potential  for 
a  single,  undivided  current? 

,  Ans.   188.502. 

29.  What  will  be  the  potential  for  the  above  mine  when  the 
current  is  divided  and  travelling  in  two  splits?   Ans.  377.004. 

30.  What  power  would  be  required  to  circulate  100000  cubic 
feet  of  air  per  minute  against  this  potential  ? 


NOTE. — This  is  toi  great  a  power  to  be  transmitted,  practically,  through  a  sec- 
tional area  of  TOO  square  feet  (2  splits) ;  we  should  use  in  this  case  from  4  to  5 
splits. 

*3i.  Employing  4  equal  splits,  in  problem  30,  what  would  be 


PRACTICAL  PROBLEMS.  153 

the  required  power ;  and  what  velocity  of  the  current  and  water- 
gauge  would  result  ? 

Ans.  70.69  h.p. ;  500  ft.  per  min. ;  4.48  ins. 

^ 

32.  Reduce  600  feet  of  air-column  to  inches  of  water-gauge. 

Ans.  8.83  ins. 

NOTE. — One  cubic  foot  of  air  will  weigh  g£s  of  the  weight  of  one  cubic  foot  of 
water  at  temperature  of  60°  F.  and  a  pressure  of  one  atmosphere  (14.7  pounds), 
its  specific  gravity  being-  0.00123,  referred  to  water  as  unity. 

NOTE. — One  or  two  problems  will  be  here  introduced,  for  the  purpose  of  show- 
ing the  actual  effect  of  the  vitiated  condition  of  the  upcast  column  ;  or,  in  other 
words,  the  back-pressure  resulting  therefrom.  These  problems  are  useful  in  cases 
of  careful  investigation,  and  should  then  always  be  taken  into  account.  For  prac- 
tical purposes,  however,  the  condition  of  the  upcast  and  downcast  columns  may 
be  considered  as  identical.  (See  Addenda.) 

33.  Suppose  a  mine  to  be  ventilated  by  means  of  a  force-fan, 
the  upcast  and  downcast  shafts  being  each  200  feet  deep,  size 
of  airways  6  x  8£  and  30,000  feet  long;  what  horse-power  will 
be  required  to  pass  100,000  cubic  feet  of  air  per  minute  through 
the  mine  in  four  splits;  not  assuming  any  differential  tempera- 
ture of  the  upcast  and  downcast  columns,  or  the  vitiated  con- 
dition of  the  upcast,  but  figuring  in   the  usual  approximate 
manner  for  practical  purposes? 

Ans.  70.69  h.p. 

34.  Assume  the  same  conditions  as  given  in  problem  33,  and 
now  suppose  the  average  temperature  of  the  downcast  (A)  to 
be  60°  F.,  that  of  the  upcast  (/i)  70°  F.,  barometric  pressure 
(£>)  30  inches,  and  a  vitiated  condition  of  the  upcast  current; 
and  determine  the  weights  of  one  cubic  foot  of  the  upcast  and 
downcast  columns  respectively. 

Ans.  Upcast  ( Wi}  0.080805  Ib. ;  downcast  ( W*)  0.077267  Ib. 

35.  What  unit  of  back-pressure  will  result  from  problem  34, 
the  upcast  and  downcast  shafts  being  each  200  feet  deep ;  and 
what  horse-power  will  now  be  required  to  pass  the  same  quantity 
of  air  per  minute  (100,000  cubic  feet)  ? 

Ans.  Unit  of  back-pressure,  0.7076  Ib. ;  actual  horse-power, 
72.841  h.p. 


154  APPENDIX. 

36.  Under  the  conditions  of  problem  34,  what  quantity  of  air 
per  minute  would   pass  were  the  horse-power  applied  70.69,  as 
figured  in  problem  33  ? 

Ans.  97,048  cu.  ft.  per  min. 

NOTE. — The  actual  unit  of  ventilating  pressure,  as  indicated  by  the  water- 
gauge,  should  correspond  under  all  conditions  of  temperature  anJ  barometric 
pressure  to  the  theoretical  unit  of  pressure,  as  derived  from  equation  XXIII  ; 
but  in  order  to  this,  and  for  careful  determination  for  purposes  of  investigation, 
the  varying  functions  of  temperature  and  barometric  pressure  must  be  taken  into 
consideration,  as  in  the  above  problems. 

FAN   FUNCTIONS. 

37.  What  is  the  efficiency  of  a  twenty-foot  fan  at  50  revolu- 
tions  per  minute  (width  of  blade  48  inches,   inner  radius  66 
inches),  which  is  yielding  a  current  of  172,270  cubic  feet  per 
minute,  under  a  three-inch  water-gauge;   temperature  at  the 
time  of  observation  being  60°  F.,  barometer  30  inches,  and  the 
air  dry? 

Ans.  go%. 

38.  If  we  now  speed  the  same  fan  up  to  100  revolutions  per 
minute,  under  the  same  atmospheric  conditions,  what  efficiency 
should  it  show ? 

Ans.  60%. 

Solution. — Referring  to  equation  XLVIL,  and  assuming  the 
temperature  and  barometric  pressure  constant,  we  see  that 

1?  varies  as  (i  —  K], 
which  gives  the  above  result. 

39.  Assuming   that   the    fan    is   working   against   the   same 
potential  in  problem  38  as  in  problem  37,  what  will  be  the  re- 
sulting quantity  and  unit  of  pressure  ;  and  what  horse-power 
will  be  developed? 

Ans.  379,220  cu.  ft.  per  m. ;  75.6  Ibs.  per  sq.  ft.  ;  868.674  h.p. 

NOTE. — The  mine-potential  in  problem  39  is  not  large  enough  for  the  increased 
power  of  the  fan  at  100  revolutions  per  minute ;  as  is  shown  by  the  resulting  unit 
of  pressure  and  the  velocity  of  the  current,  which  would  be  almost  32  feet  per 
second.  The  potential  should  be  increased,  in  this  case,  by  splitting  the  air-cur- 
rent, until  a  normal  water-gauge  and  a  moderate  velocity  is  obtained. 


OF  THE 

tJNIVERSITT 


PRACTICAL   PROBLEMS:  155 


40.  What  is  the  value  of  the  fan-constant  (<r2)  in  problems  37 
and  38?     (See  equation  XLVII.) 

Ans.  0.000002312. 

41.  What  is  the  value  of  the  fan-constant  when  the  yield  and 
water-gauge  indicate  an  efficiency  of  85  per  cent  at  50  revolu- 
tions, or  40  per  cent  at  100  revolutions  per  minute,  tempera- 
ture being  60°  F.  and  the  barometer  30  inches  ? 

Ans.  0.000003468. 

42.  Give  the  value  of  the  fan-constant  under"  the  same  condi- 
tions, when  the  efficiency  is  95  per  cent  at  50  revolutions,  or 
80  per  cent  at  100  revolutions  per  minute? 

Ans.  0.000001156. 

43.  Find  the  maximum  effective  speed,  under  the  conditions 
of  problem  42;  i.e.,  when  the  fan-constant  is  o.oooooi  156,  the 
temperature  being  60°  F.  and  the  barometer  30  inches;  or,  in 
other  words,  at  what  speed  will  the  fan  yield  the  greatest  quan- 
tity of  air  per  minute  ? 

Ans.  182.6  rev's  per  m. 

44.  Find  the  limit  of  speed  of  the  same  fan,  under  the  same 
conditions;  i.e.,  at  what  speed  will  this  particular  fan  cease  to 
throw  any  air  under  the  atmospheric  conditions  mentioned? 

Ans.  223.6  rev's  per  m. 

45.  Find  the  maximum  effective  speed  and  the  limit  of  speed 
for  the  fan  mentioned  in  problem  40,  under  the  same  atmos- 
pheric conditions? 

Ans.  Max.  effect,  speed,  129.1  rev's  perm.;  limit  of  speed, 
158.1  rev's  per  m. 

NOTE.  —  A  fan  will  rarely  ever  give  as  low  an  efficiency  as  that  mentioned  in 
problem  41.  The  efficiency  will  frequently  exceed  that  given  in  problem  42.  The 
Murphy  type  of  fans  may  present  a  higher  efficiency  than  that  afforded  by  the 
straight-paddle  fan  ;  but  their  yield  is  not  represented  by  equations  XXXVIII- 
XL.  The  backward  curvature  of  the  blades,  resulting  in  a  loss  of  rotary  motion 
to  the  air,  weakens  the  pressure  incident  to  speed.  This  type  of  fan  therefore 
requires  a  higher  speed  for  the  same  yield.  (See  Addenda.) 

46.  We  are  opening  a  mine  to  be  ventilated  by  a  force-fan, 
straight-paddle  ;  and  we  wish  to  provide  for  the  circulation  of 


156  APPENDIX. 

100,000  cubic  feet  of  air  per  minute,  in  four  equal,  separate 
splits  ;  size  of  airways  (6  x  8)  and  50,000  feet  long.  What  size  of 
fan  should  we  adopt  ? 

Ans.  Diam.  of  fan,  18.9  ft.;  width  of  blade,  7.1  ft.;  exp.  of 
casing.  4.7  ft. 

47.  In  the  last  problem,  what  will  be  the  speed  of  the  fan  at 
which  it  will  throw  the   100,000  cubic  feet  of  air  per  minute, 
under  the  conditions  mentioned,  temp.  60°  F.,  barom.,  30"  ? 

Ans,  50.3  rev's  per  m. 

48.  Assuming  that  the  value  of  the  fan-constant  of  this  fan 
is  0.000002312,  what  quantity  of  air  per  minute  will  it  circulate 
in  the  mine  mentioned,  in  four  equal  splits,  when  running  at  a 
speed  of    100  revolutions  per   minute,  the   temperature  being 
60°  F.  and  the  barometer  30  inches? 

Ans.  215,745  cu.  ft. 

49.  What  would  be  the  velocity  of  the  intake  of  the  fan  in  the 
last  problem? 

Ans.  About  19  ft.  per  sec. 

50.  What  is  the  velocity  of  the  blade-tips  and  the  peripheral 
flow,  respectively,  in  each  of  the  cases  mentioned  in  problems 
46  and  48? 

Ans.  First  case:  Blade-tips  49.8  ft.  per  sec.,  per  flow  50.0  ft. 
per  sec. ;  second  case :  Blade-tips  99  ft.  per  sec.,  periph.  flow 
108  ft  per  sec. 

51.  What  will  be  the  horse-power  of  this  same  fan  running  at 
a  speed  of  60  revolutions  per  minute,  assuming  the  fan-constant 
to  be  0.0000023 1 2,  temperature  o°  F.,  and  the  barometer  30  inches ; 
and  what  will  be  its  efficiency  ? 

Ans.  252.231  h.p. ;  efficiency,  87.27$. 

52.  What  will  be  the  horse-power  of  the  same  fan,  running  at 
the  same  speed,  when  the  temperature  is  90°  F.  and  the  bar- 
ometer 28  inches,  and  what  the  efficiency? 

Ans.   188.727  h.p.  ;  efficiency,  83.68^. 


PRACTICAL    PROBLEMS.  157 

53.  At  what  speed  will  it  be  necessary  to  run  the  fan  under 
the  conditions  prevailing  in  problem  52,  in  order  to  maintain 
the  power  developed  in  problem  51  ? 

Ans.  65.1  revs,  per  min. 

54.  What  is  the  horse-power  of  a  1 2-foot  Murphy  fan,  blades 
3x3  ft.,  inclination  of  blade  to    the  radial  at  the  centre  of 
gravity  30  degrees,  fan-constant  0.000001156,  at  a  speed  of  100 
revolutions  per  minute,  when  the  atmospheric  temperature  is 
60°  F.  and  the  barometric  pressure  29  inches  ? 

Ans.  102.314  h.p. 

55.  What  would  be  the  horse-power  of  a  straight  paddle  fan 
of  the  same  dimensions  and  having  the  same  fan-constant,  at 
the  same  speed  and  under  the  same  atmospheric  conditions? 

Ans.  111.538  h.p. 

56.  What  is  the  horse-power  of  a  1 6-foot  straight-paddle  fan, 
blades  5  feet  wide  and  42  inches  deep,  running  at  a  speed  of  50 
revolutions  per  minute,  and  showing  an  efficiency  of  90$  at  this 
speed ;  temperature  being  60°  F.  and  the  barometric  pressure 
30  inches  ? 

Ans.  41.369  h.p. 

57.  What  will  be  the  horse-power  of  the  same  fan  under  the 
same  atmospheric  conditions,  at  a  speed  of  100  revolutions  per 
minute ;  and  what  will  be  its  efficiency  at  this  speed  ? 

Ans.  441. 263  h.p. ;  efficiency  60%. 

58.  If  a  12-foot  fan,  blades  3x3  feet,  running  at  a  uniform 
speed  of  50  revolutions  per  minute  under  a  2-inch  water-gauge, 
yields  24,048  cubic  feet  of  air  per  minute  at  a  temperature  of 
60°  F.  and    a   barometric   pressure  of   29   inches,    what  is  its 
efficiency  and  what  is  the  fan-constant? 

Ans.  Efficiency,  87$ ;  fan-constant,  0.0000029. 

59.  Suppose  we  wish  to  arrange  for  the  circulation  of  a  cur- 
rent of  100,000  cubic  feet  of  air  per  minute,  travelling  in  four 
separate  splits,  through  an  airway  (6  x  8-J-  feet)  60,000  feet  long ; 


158  APPENDIX. 

what  size  of  straight-paddle  fan  should  we  adopt,  and  at  what 
general  speed  should  the  fan  be  run  to  accomplish  this  work? 

Ans.  Diam.  of  fan,  18.35  ft- 1  width  of  blade,  6.88  ft.;  exp.  of 
casing,  4.6  ft. ;  diam.  of  eye,  10  ft. ;  net  intake  area,  two  eyes, 
1 10  sq.  ft.  ;  speed  of  fan,  54.9  revs,  per  min. 


SPLITTING  THE   AIR. 

60.  Suppose  two  airways  having  the  same  sectional  dimen- 
sions, and  whose  lengths  are  respectively  1600  and  5400  feet  longt 
to  be  open  to  the  free  passage  of  the  circulating  current ;  how 
will  an  intake  current  of  10,000  cubic  feet  of  air  per  minute 
divide  itself  between  these  two  entries? 

Ans.  6,000  cu.  ft.  ;  4,000  cu.  ft. 

*/  /  <*»•>?    $^ 

61.  What  is  the  horse-power  of  a  current  of  100,000  cubic 

feet  per  minute,  circulating  in  four  equal  splits;  size  of  airways 
(6  x  8£)  feet;  total  length  25,000  feet? 

Ans.   58.908  h.p. 

62.  Find  the  total  horse-power  of  the  following  splits  when 
box-regulators  are  used : 

Split  A.  6x8^  ft.,  5,000  ft.  long,  10,000  cu.  ft. 
"  B.  "  "  6,000  "  "  15,000  "  " 
"  C.  "  "  8,000  "  "  20,000  "  " 
"  P.  "  "  10,000  "  "  18,000  "  " 

Ans.  38.6  h.p. 

63.  Find  the  total  horse-power  of  the  same  splits,  using  the 
j  her  form  of  regulator. 

Ans.  22.253  h.p. 

64.  What  will  be  the  sizes  of  the  openings  in  the  box-regula- 
tors in  problem  62  ?     (See  Addenda.) 

Ans.   Split  A,  247  sq.  in.;  split  B,  480  sq.  in.;  split  D,  1491 
sq.  in. 

65.  Taking  the  width  of  the  airway  (8i  feet)  as  100  inches, 


PRACTICAL   PROBLEMS.  159 

what  will  be  the  respective  widths  of  the  openings  at  the  mouths 
of  the  several  splits,  in  problem  63  ? 

Ans.  Split  A,  3.38  in. ;  split  B,  13.75  in.  ;  split  C,  43.37  in.  ; 
split  D,  39.50  in. 

66.  Suppose  a  vein  dipping  at  an  angle  of  30  degrees  to  be 
ventilated  in  two  main  splits.     The  headings  or  levels  are  400 
feet  apart,  measured  upon  the  slope  ;  the  size  of  the  dip-split  is 
6  x  S£  feet  and  10,000  feet  long;    temperature  of  the    intake 
50°  F.and  of  the  return  70°  F.,  barometer  3omches.     The  regu- 
lators are  arranged  so  that  the  dip-split  takes  20,000  cubic  feet 
of  air  per  minute,  while  the  level-split  takes  30,000  cubic  feet. 
How  much  air  per  minute  will  each  split  take  when  the  total 
quantity  of  air  furnished  per  minute  to  the  mine  has  been  re- 
duced to  40,000  cubic  feet,  supposing  that  no  change  is  made  in 
the  regulators  ? 

Ans.  Level-split,  23,555  cu-  ft- 1  dip-split,  16,445  cu-  ft- 

67.  In  the  last  problem,  what  quantities  of  air  per  minute 
would  each  split  take  were  the  circulation  to  be  increased  from 
50,000  to  60,000  cubic  feet  per  minute  ? 

Ans.  Level-split,  36,444  cu.  ft.  ;  dip-split,  23,556  cu.  ft. 

GENERAL   PROBLEMS. 

68.  Suppose  we  have  a  current  of  50,000  cubic  feet  of  air  per 
minute  travelling  in  two  splits;  size  of  airways  6  x  8^  feet  and 
the  entire  length  30,000  feet ;  if  a  fall  occur  upon  the  main  air- 
way before  the  split  is  reached,  so  as  to  reduce  the  sectional  area 
of  the  same  from  50  to  25  square  feet,  the  power  of  the  motor 
remaining  the  same,  what  quantity  of  air  per  minute  will  pass 
over  the  fall  and  through  the  mine,  assuming  a  temperature  of 
60°  F.  and  a  barometer  of  30  inches  ? 

Ans.  49,437  cu.  ft. 

69.  In  a  certain  mine  a  current  of  50,000  cubic  feet  per  minute 
is  passing  in  two  splits  of  the  following  size : 

Split  A.  6  x  8£  ft.,   10,000  ft.  long. 
B.  6  x  10  "    40,000  "      " 


l6o  API'K.NPIX. 

If  we  now  introduce  a  box-re^ulaloi  having  an  opening  of  60.56 

•.i|ii.in-  m.  In  ..  into  split  A,  \\li.ii  .|ii.iiiiii\  .-I  nil  will  thru  pass 
in  i'.ii  li  split  per  minute,  assuming  (hut  (In-  power  is  incicased 
to  in.iiui.iiii  the  (low  ol  ,.'..«..,  i  ,  nl'i.  (ret  in  the  main  intake, 
lempciatnic  (>o"  I1'.,  and  barometer  \o  inches? 

.•///.v.    Split  A.  10.000  en.  It.  ;  split   I),  40,000  CU,  I't. 

70.  In  the  last  problem,  what  per  eent  of  the  power  is  lost  in 
the  regulator  ;  ^ive  also  the  horse-power  of  the  circulation  in 
the  two  methods  ? 

„'/«.*.  49.66^  ;  old  method,  440.828  h.p.  ;  new  method,  224.922 


71.  If  a  (HM'tain  motor  is  nipablr  of  circulating  a  current  of 
•.'..'.'.>  en  hie  feet  per  minute  through  a  cei  tain  mine,  and  a  not  her 
motor    ^O,IHH\  cubic   leet     per  minute   in   the  same   mine,    eaeh 
working  alone  l>nt    umlci    like  condii  ions,  wh.il  (jnantitv  of  air 
per  minute  will  result    horn   their  combined   artion   nnder  the 
same  conditions  ?     (Sec  equation  XXX11I.) 

.'I  MX.     32,  '/I  I    CU.  ft. 

72.  If  the  motor  first  mentioned  above,  in  performing  its  work 
of  circulating  ;O.IHX>  cnbic  feet  of  air  per  minute  through  a  cer- 
tain  mine,  yields  a   water  ^anj^e  ol    ,'.  inches,  the  water  gau^e 
yii'lded   by  the   scctMul   motoi    in   the  circulation   of   the   30,000 
cubic  leet  of  air  per  minute  will  be,|J  inches;  what  will  be  the 
water-^au^e  when  the  two  motors  are  woikin^  together  nnder 
the  same  conditions  ? 

Ann.   5.35  ins. 


AI)I>KNI)A. 


WK  will  consider  here  Hurli  other  conditions  prevailing  in  the 
pit  as  affect  to  a  greater  or  less  decree  the  ventilation  of  the* 
Name,  but  whirl)  arc  ignored  in  our  ordinary  calculations. 
These  arc  interesting,  however,  as  matters  of  information,  and 
are  quite  essential  in  all  cases  of  careful  investigation.  We 
refer  now  to  the  change  in  the  weight  of  the  downcast  column, 
due  to  the  prcHHiire  of  the  pit,  in  eornpressive  ventilation  ;  and 
to  the  variation  in  the  weight  of  the  upcast  column,  arising 
fiom  the  saturation  of  the  return  current.  Also  Much  other 
cases  will  be  here  introduced  and  other  formulas  developed  an 
require  to  some  extent,  a  knowledge  of  the  higher  mathematics. 
These  have  been  eliminated  from  the  main  body  of  the  book, 
because  they  are  not  essential  to  a  practical  knowledge  of  the 
subject.  ;  but.  the  work  would  not  be  complete  without,  refer- 
ence to  them. 

Condition  of  Current  due  to  Pressure  and  Saturation.  There 
are  three  conditions  of  the  air  in  the  pit,  and  the  weight  of  thin 
air  is  therefore  represented  by  three  dilTerent  expressions,  ns 
follows  : 

Kxhaustive  downcast  : 


w, 

Compressive  downcast  : 


7<>.7(45<H 
Upcast  (2  cases)  : 


I-439W  -  0/4)  4-  0.82630,, 
~ 


161 


l62  ADDENDA. 

In  the-case  of  the  upcast  column  two  conditions  may  arise. 
First,  as  in  the  case  of  a  dry  furnace-shaft,  the  temperature  /4, 
at  which  the  air  was  saturated,  is  lower  than  the  temperature 
/i,  the  average  temperature  of  the  upcast.  Second,  as  in  the 
case  of  a  wet  furnace-shaft,  or  any  case  of  fan-ventilation  or 
otherwise,  where  the  upcast  column  is  not  heated,  the  tempera- 
ture (/4)  at  which  the  air  is  saturated  will  be  equal  to  the  tem- 
perature of  the  shaft,  the  excess  of  moisture  being  deposited 
all  the  way  up  the  shaft,  as  the  current  is  cooled  in  its  ascent. 
The  average  temperature  of  saturation  will  then  be  identical 
with  the  average  temperature  of  the  shaft.  The  temperature  of 
saturation  can  never  be  greater  than  the  temperature  of  the 
shaft,  as  the  moisture  would  then  be  at  once  deposited. 

The  above  three  expressions  are  developed  as  follows : 
Expression  (i)  is  a  simple  case,  and  gives  the  weight  of  one 
cubic  foot  of  dry  downcast  air  under  the  barometric  pressure 
B,  and  the  average  temperature  of  the  downcast  shaft  /2 ;  it 
is  derived  from  equation  (I).  This  expression  is  applicable  only 
to  the  exhaustive  system,  where  natural  draft,  furnace,  or  ex- 
haust-fan is  in  use. 

Expression  (2)  applies  to  the  compressive  system  of  ventila- 
tion, and  gives  the  weight  of  one  cubic  foot  of  dry,  downcast 
air,  subject  to  the  barometric  pressure  B  and  the  theoretical 
unit  of  ventilating  pressure  p,  due  to  the  resistance  of  the 
rubbing  surface  of  the  airways,  and  expressed  by  equation 
(XXIII),  and  a  further  back-pressure,  arising  from  the  vitiated 
condition  of  the  upcast  current.  This  unit  of  back-pressure, 
due  to  the  heaviness  of  the  upcast  current,  is  readily  found  by 
deducting  the  weight  of  one  cubic  foot  of  air,  as  given  by  ex- 
pression (i),  from  the  weight  of  one  cubic  foot  of  air  derived 
from  expression  (3) ;  and  multiplying  the  excess  or  difference 
thus  found  by  the  motive  height  /i,  which  will  give  the  unit  of 
back-pressure  from  this  cause  very  approximately.  Now,  equa- 
tion (i)  give"  the  weight  of  one  cubic  foot  of  air  under  the 
barometric  pressure  JS,  which  pressure  is  expressed  in  inches 
of  mercury  ;  hence,  in  the  present  instance,  we  must  reduce  the 
unit  of  ventilating-pressure  p,  and  the  unit  of  back-pressure 
//(wi  —  wa)  to  inches  of  mercury,  and  add  these  results  to  the 
B  of  equation  (i).  We  see  by  referring  to  equation  (XXXVI) 


ADDENDA.  163 

that  one  inch  of  water-gauge  represents  a  unit  of  pressure  of 
5.2  pounds;  and  since  the  specific  gravity  of  mercury  is  13.596, 
it  follows  that  one  inch  of  mercury  represents  a  unit  of  pressure 
of  70.7  pounds.  Hence,  dividing  these  units  of  pressure  by  70.7, 
and  adding  the  results  to  B,  and  substituting  for  B  in  equation 
(i),  and  reducing,  we  obtain  expression  (2). 

Expression  (3)  gives  the  weight  of  one  cubic  foot  of  the  viti- 
ated upcast  current,  and  is  obtained  by  adding  together  the 
following  expressions  (see  equations  (i),  (3),  (5),  (XLIV)) : 

(Nitrogen,  i  cu.  ft.  upcast).       — — .      .     (4) 

459+A 

(Carb.  acid,  i  cu.  ft.  upcast).    °-4'9K*  -  0/J  (5) 

459+A 

(Aq.  vapor,  i  cu.  ft.  upcast). -.       ...     (6) 

459+^1 

Box-regulators.— There  has  always  been  experienced  some 
difficulty  in  estimating  exactly  the  influence  which  these  regu- 
lators exert  upon  the  current  of  air,  and  in  figuring  the  size  of 
opening  in  such  a  regulator  which  will  give  the  required 
amount  of  air  in  each  of  the  splits  in  question.  As  a  matter 
of  fact  in  practice,  we  set  up  the  regulator  and  move  the  shutter 
to  and  fro,  until  the  desired  proportion  of  air  is  obtained  ;  and 
this  practice  is  correct,  as  the  varying  conditions  of  the  air- 
courses  are  constantly  introducing  factors  which  modify  the 
results.  Nevertheless,  it  is  interesting  to  investigate  the  prin- 
ciples which  control  the  flow  of  the  air-current  through  the 
opening. 

To  begin  with,  we  recognize  that  this  form  of  regulator  is 
introduced  into  that  one  of  two  splits  which  is  taking  more  air 
than  the  desired  proportion,  in  order  to  obstruct  the  flow  in 
that  split.  The  obstruction  thus  introduced  creat^  an  increase 
of  pressure  behind  the  regulator,  which  increase  is  due  to  the 
regulator  alone,  as  distinct  from  the  mine-pressure  at  this  point, 
or  the  pressure  incident  to  the  flow  of  the  current  ahead  of  the 
regulator.  We  note  that  the  pressure  due  to  the  regulator  is 
unbalanced  by  anything  on  the  other  side;  it  is,  in  other 


164  ADDENDA. 

words,  the  pressure  which  animates  the  flow  through  the  open- 
ing of  the  regulator,  or  it  is  the  pressure  which  will  take  the 
current  through  this  opening.    It  will  not  do  any  more  ;  it  does 
not  contribute  to  the  movement  of  this  current  ahead  of  the 
regulator;  the  mine-pressure  does  that;   it  simply  overcomes 
the  regulator,  and  places  the  current  ahead  of  the  regulator 
under  the  same  conditions  as  would  exist  were  the  regulator 
not  there.     We  will  first  find  what  this  pressure  due  to  the 
regulator  is,  in  terms  of  the  quantity  of  air  passing  through  the 
opening  and  the  size  of  the  opening  (we  are  speaking  now  of  the 
pressure  per  square  .foot,  or  the  unit  of   pressure).     Having 
found  this  unit  of  pressure  (/)  due  to  the  regulator,  we  will 
multiply  it  by  the  sectional  area  of  the  airway  to  obtain  the 
total  pressure  due  to  the  regulator,  and  then  again  multiply  this 
result  by  the  velocity  of  the  current,  which  will  give  the  work 
absorbed  or  lost  in  the  passage  of  the  regulator  ;  or,  we  may 
multiply  at  once  by  the  quantity  of  air  passing  per  minute,  and 
obtain  the  same  result. 

Pressure  due  to  Box-regulator.  —  The  flow  of  a  current  of  air 
through  the  opening  in  a  box-regulator  is  identical  with  the 
flow  of  any  fluid  through  an  orifice  in  a  thin  plate  ;  and,  as  we 
have  seen  in  Chapter  X,  the  velocity  of  the  flow  is  represented 
by  the  equation, 

z>=4/2^,     ........     (i) 

from  which  we  have, 


<»> 


in  which  v  is  the  velocity  of  the  flow  through  the  orifice  in  feet 
per  second.  Hence  we  have  for  the  quantity  of  the  flow  per 
minute  Q,  through  the  orifice  or  opening  ain 

Q  =  6oa,,v,    ........     (3) 

from  which  we  may  write, 


(4) 


But  in  all  cases  of  the  flow  of  a  fluid  through  an  opening  in  a 
thin  plate  there  results  a  contraction  of  the  area  of  the  flow 


ADDENDA.  165 

just  outside  of  the  orifice,  which  reduces  the  quantity  of  the 
flow.  This  contraction  of  area  is  known  in  physics  as  the  vena 
contracta,  and  varies  according  to  the  form  of  the  orifice,  and 
in  our  case,  where  the  orifice  or  opening  is  within  an  airway, 
and  bears  a  considerable  relation  to  the  sectional  area  of  such 
airway,  the  contraction  of  area  will  vary  according  to  the  size 
of  the  opening,  relative  to  the  sectional  area  of  the  airway  ;  thus 
the  contraction  will  diminish  as  the  area  of  the  opening  ap- 
proaches that  of  the  airway,  and  vice  versa.  The  coefficient  of 
this  contraction  may,  therefore,  be  represented  very  approxi- 
mately for  our  purpose  by  the  seventh  root  of  the  ratio  ex- 
pressed by  dividing  the  area  of  the  opening  by  the  area  of  the 
airway,  or  by  the  expression 


(5) 


Hence,  the  true  area  of  the  flow  will  be  represented  by  the  ex- 
pression, 

i/*»aa     or     i/S.  (6) 

r       a  r       a 

Squaring  this  expression,  and  substituting  it  for  a*  in  equation 
(4),  we  have, 


3600 


Now  h  in  equation  (2)  is  the  generative  height ;  it  is  the  height 
of  the  surface  of  the  fluid  above  the  orifice  (see  Fig.  XIII.),  it 
is  the  head  of  air-column.  Hence,  referring  to  equation  II., 
and  substituting  this  value  for  h  in  equation  (2)  above,  and  sub- 
stituting for  v  in  the  same  equation  its  value  as  taken  from 
equation  (7)  above,  solving  with  respect  to/,  and  reducing,  we 
have  for  the  unit  of  pressure  due  to  the  regulator, 

P  =  0.00000572-^-y  ^1-Q\   .     .     .     (LXV) 


Work  due  to  Box-regulator. — To  find  the  work  absorbed  or 
lost  in  the  passage  of  this  form  of  regulator,  we  multiply  the 


l66  ADDENDA. 

above  unit  of  pressure  (/)  due  to  the  regulator  by  the  quantity 
of  air  (0  passing  per  minute  and  we  have 

«  =  0.00000572^-^^2=.    .     .     (LXVI) 

Illustration. — Suppose  now  that  we  have  in  a  certain  mine  a 
current  of  10,000  cubic  feet  per  minute  travelling  in  two  splits 
as  follows : 

Split  A.  6  x  8£,  5000  ft.  long. 
"     B.      "         8000  "      " 

If  no  regulator  is  introduced  the  natural  division  of  the  air 
would  send  5391  cubic  feet  into  split  A  and  4609  cubic  feet  into 
split  B.  Now  suppose  we  desire  to  throw  6000  cubic  feet  of  this 
current  into  split  B,  what  size  of  opening  in  a  box-regulator 
introduced  into  split  A  will  accomplish  this  result?  We  have 
seen  in  Chapter  IX  that  the  unit  of  work  pv  at  the  point  of 
split  or  the  work  transmitted  by  one  square  foot  of  sectional 
area  to  each  of  the  several  splits  is  the  same,  reacting  against 
each  other,  and  as  the  exposed  areas  of  the  two  splits  in  this 
case  are  the  same,  the  total  work  performed  in  each  must  be  the 
same.  Now  we  ascertain  from  equation  (XIII)  the  work  that 
will  be  consumed  in  circulating  6000  cubic  feet  of  air  per  minute 
through  split  B,  and  this  work  (8600  foot-pounds)  will  be  also 
the  work  applied  to  split  A,  that  is  to  say,  the  work  that  is  re- 
sponsible for  the  circulation  of  4000  cubic  feet  of  air  in  this  split 
per  minute  plus  the  work  lost  in  the  passage  of  the  regulator. 
Finding  from  equation  (XIII)  the  work  absorbed  in  this  split 
by  the  circulation  of  the  4000  cubic  feet  of  air  (i  592  foot-pounds) 
and  deducting  this  from  the  total  work  applied  (8600  foot- 
pounds) we  obtain  7008  foot-pounds  as  the  work  absorbed  by 
the  regulator.  Finally,  substituting  this  value  for  u  in  equa- 
tion (LXVI),  and  assuming  a  temperature  of  60°  F.  and  a  bar- 
ometric pressure  of  30  inches,  giving  to  a  and  Q  their  numerical 
values  and  reducing,  we  obtain  for  the  value  of  au , 

ait  =  380  sq.  ins., 

or  an  opening  of  19^  inches  square.  This  problem,  as  well  as 
many  others  of  this  nature,  is  very  easily  worked  by  the  aid  of 


ADDENDA.  167 

logarithms,  but  on  account  of  the  high  powers  of  some  of  the 
quantities  can  only  be  approximated  by  the  methods  of  arith- 
metic. We  would  recommend  the  use  of  logarithms  in  the 
solution  of  all  problems  in  mine  ventilation. 

Quantity  of  Air  passing  a  Box-regulator.  —  We  may  write  for 
the  work  performed  in  each  split  as  follows  : 

Work  in  split  A.  (0.00000572^^-  j/  ~-6  +  *^Q*. 

ks 

Work  in  split  B.  —  (Qf. 
ai 

Then,  equating  these  works  and  solving  with  respect  to  Q, 
the  quantity  of  air  passing  the  regulator  per  minute,  and 
writing  the  potential  X  for  its  value  (see  equation  (XXVI  I)), 
we  have, 

=       (LXVII) 


Effect  of  Fall  upon  Main  Air-course.  —  When  a  fall  occurs 
upon  the  main  air-course  so  as  to  seriously  obstruct  the  flow  of 
the  air-current  the  amount  of  the  flow  after  the  fall  may  be 
figured  from  equation  (LXVII),  by  Q,  represent  the  quantity  of 
air  passing  in  the  airway  before  the  fall  occurred,  and  aif,  the 
reduced  sectional  area  of  the  airway  at  the  fall  ;  in  this  case  X, 
will  be  equal  to  X. 

Effect  of  Inclination  or  Curvature  of  Blade  of  a  Fan.—  In  all 
fans  having  inclined  or  curved  blades,  the  reaction  of  the  air 
against  the  blade  being  normal  to  the  blade  is  no  longer 
tangential  to  the  rotary  motion  of  the  fan,  and  as  a  consequence 
there  results  a  loss  in  the  accelerative  velocity  imparted  to  the 
air  by  virtue  of  its  revolution  in  the  fan! 

Let  us  for  a  moment  suppose  the  air  contained  in  one  section 
of  a  fan  to  be  concentrated  at  the  point  a  upon  the  path  of  its 
centre  of  gravity.  Now,  the  point  a  is  impelled  or  moved 
forward  by  the  motion  of  the  blade  in  the  direction  ab 
tangential  to  the  rotary  path  of  the  blade,  and  the  force  which 


i68 


ADDENDA. 


impels  it  is  the  velocity  with  which  the  blade  is  moving,  but 
the  direction  of  this  motion  or  of  the  impelling  force  ab  not 
being  normal  to  the  surface  of  the  blade  at  this  point,  there 
results  a  sliding  (ac)  of  the  point  along  the  surface  of  the  blade, 
and  the  resultant  of  these  two  motions  is  ad\  consequently  the 
point  a  has  been  moved  outward  in  a  radial  direction,  or  nor- 
mal to  the  tangent  ab,  a  distance  (ed).  Now,  inasmuch  as  the 
power  of  the  fan  is  derived  from  the  centrifugal  force  incident 
to  the  revolution  of  the  weight  of  air  which  we  have  considered 
as  concentrated  at  its  centre  of  gravity  a,  and  inasmuch  as  this 


FIG.  XVII. 

centrifugal  force  is  dependent  for  its  development  upon  the 
retention  of  the  point  a  in  the  rotary  path,  any  movement  or 
yielding  in  a  radial  direction,  due  to  mechanical  influence,  will 
result  directly  in  a  loss  to  the  centrifugal  force,  as  expressed  by 
the  equation  (3-XXXVIII) ;  it  will  be  readily  noted  that  while 
this  movement  in  a  radial  direction  reduces  the  acceleration 
due  to  the  centrifugal  force  and  therefore  the  measure  of  this 
force  (fni),  it  does  not  reduce  the  distance  through  which  this 
force  acts ;  it  only  makes  a  part  of  such  distance  due  to  the 
mechanical  influence  of  the  inclined  blade. 

Now,  referring  again  to  Fig.  (XVII),  we  see  that  for  any 
infinitesimal  period  of  time  the  tangent  ab  will  correspond  to 
and  form  a  part  of  the  circle  described  by  the  points,  and  will 
therefore  represent  the  space  passed  over  by  this  point  in  such 


ADDENDA.  169 

infinitesimal  time.     Denoting  this  space  by  v,  we   may  write 
from  the  figure 

ed  =  v  sin  a  cos  a,       ......     (i) 

ed  representing,  as  we  have  seen,  the  loss  to  the  accelerative 
velocity  for  an  infinitesimal  period  of  time. 

Referring  to  equation  (6-XXXVIII),  and  dividing  by  two,  to 
obtain  the  space  passed  over  by  the  air  considered  as  concen- 
trated at  the  point  a  under  the  accelerative  influence  in  one 
second  of  time,  we  have  the  expression 

0.005483^/2',        .......     (2) 

and  for  the  infinitesimal  period  of  time  referred  to  above  we 
have, 


or,  reducing,  we  have, 

0.052359?*  .........    (4) 

This  last  expression  represents  the  space  passed  over  by  the  air 
considered  as  concentrated  at  the  point  a  under  the  accelera- 
tive influence  of  a  straight-paddle  blade  in  the  same  infinitesimal 
period  of  time. 

Then,  finally,  by  dividing  expression  (i)  by  expression  (4)  we 
obtain  the  ratio  expressing  the  loss  to  the  accelerative  velocity 
and  consequently  to  the  centrifugal  force. 


.....    (LXVIII) 


This  expression  (LXVIII)  represents  the  ratio  by  which  the  cen- 
trifugal force  of  the  revolved  air  is  weakened,  and  by  which  also 
the  power  of  the  fan  is  impoverished.  Any  particle  of  air,  as 
#,  for  example,  in  its  passage  through  the  fan  moves  under  the 
influence  of  two  forces  ;  one  of  these  forces  (the  mechanical 
revolution  of  the  fan)  impels  it  in  a  direction  normal  to  the 
surface  of  the  blade  ;  the  other  (the-centrifugal  force)  is  a  radial 


I/O  ADDENDA. 

force;  as  a  result  of  the  combined  action  of  these  two  forces, 
the  particle  moves  in  a  spiral  path,  revolving  with  the  fan-blades, 
but  ever  approaching  the  outer  circumference,  where  it  is 
thrown  off.  The  radius  of  curvature  of  this  spiral  will  be 
greater,  and  consequently  the  centrifugal  force  developed  by 
the  revolution  will  be  less,  as  the  fan-blade  is  more  inclined. 


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